The only city in the world that can lay claim to straddling two continents, Istanbul—once known as Constantinople, capital of the Byzantine and then the Ottoman Empire—has for centuries been a bustling metropolis with one foot in Europe and the other in Asia. Istanbul embraces this enviable position with both a certain chaos and inventiveness, ever evolving as one of the world’s most cosmopolitan crossroads. It’s often said that Istanbul is the meeting point of East and West, but visitors to this city built over the former capital of two great empires are likely to be just as impressed by the juxtaposition of old and new. Office towers creep up behind historic palaces, women in chic designer outfits pass others wearing long skirts and head coverings, peddlers’ pushcarts vie with battered old Fiats and shiny BMWs for dominance of the noisy, narrow streets, and the Grand Bazaar competes with modern shopping malls. At dawn, when the muezzin's call to prayer resounds from ancient minarets, there are inevitably a few hearty revelers still making their way home from nightclubs and bars. Most visitors to this sprawling city of more than 14 million will first set foot in the relatively compact Old City, where the legacy of the Byzantine and Ottoman empires can be seen in monumental works of architecture like the brilliant Aya Sofya and the beautifully proportioned mosques built by the great architect Sinan. Though it would be easy to spend days, if not weeks, exploring the wealth of attractions in the historical peninsula, visitors should make sure also to venture elsewhere in order to experience the vibrancy of contemporary Istanbul. With a lively nightlife propelled by its young population and an exciting arts scene that’s increasingly on the international radar—thanks in part to its stint as the European Capital of Culture in 2010—Istanbul is truly a city that never sleeps. It’s also a place where visitors will feel welcome: Istanbul may be on the Bosphorus, but at heart it’s a Mediterranean city, whose friendly inhabitants are effusively social and eager to share what they love most about it.

For better or worse, it can be difficult to reach Patmos—for many travelers, this lack of access is definitely for the better, since the island retains the air of an unspoiled retreat. Rocky and barren, the small, 34-square-km (21-square-mi) island lies beyond the islands of Kalymnos and Leros, northwest of Kos. Here on a hillside is the Monastery of the Apocalypse, which enshrines the cave where St. John received the Revelation in AD 95. Scattered evidence of Mycenaean presence remains on Patmos, and walls of the classical period indicate the existence of a town near Skala. Most of the island's approximately 2,800 people live in three villages: Skala, medieval Chora, and the small rural settlement of Kambos. The island is popular among the faithful making pilgrimages to the monastery as well as with vacationing Athenians and a newly growing community of international trendsetters—designers, artists, poets, and “taste gurus” (to quote Vogue’s July 2011 write-up of the island)—who have bought homes in Chora. These stylemeisters followed in the footsteps of Alexandrian John Stefanidis and the English artist Teddy Millington-Drake who, in the early ’60s, set about creating what eventually became hailed as one of the most gorgeous island homes in the world. The word soon spread thanks to their many guests (who included Jacqueline Kennedy Onassis) but, happily, administrators have carefully contained development, and as a result, Patmos retains its charm and natural beauty—even in the busy month of August.

Early travelers described Rhodes as a town of two parts: a castle or high town (Collachium) and a lower city. Today Rhodes town—sometimes referred to as Ródos town—is still a city of two parts: the Old Town, a UNESCO World Heritage site that incorporates the high town and lower city, and the modern metropolis, or New Town, spreading away from the walls that encircle the Old Town. The narrow streets of the Old Town are for the most part closed to cars and are lined with Orthodox and Catholic churches, Turkish houses (some of which follow the ancient orthogonal plan), and medieval public buildings with exterior staircases and facades elegantly constructed of well-cut limestone from Lindos. Careful reconstruction in recent years has enhanced the harmonious effect.

Undoubtedly the most extraordinary island in the Aegean, crescent-shape Santorini remains a mandatory stop on the Cycladic tourist route—even if it's necessary to enjoy the sensational sunsets from Ia, the fascinating excavations, and the dazzling white towns with a million other travelers. Called Kállisti (the "Loveliest") when first settled, the island has now reverted to its subsequent name of Thira, after the 9th-century-BC Dorian colonizer Thiras. The place is better known, however, these days as Santorini, a name derived from its patroness, St. Irene of Thessaloniki, the Byzantine empress who restored icons to Orthodoxy and died in 802. You can fly conveniently to Santorini, but to enjoy a true Santorini rite of passage, opt instead for the boat trip here, which provides a spectacular introduction. After the boat sails between Sikinos and Ios, your deck-side perch approaches two close islands with a passage between them. The bigger one on the left is Santorini, and the smaller on the right is Thirassia. Passing between them, you see the village of Ia adorning Santorini's northernmost cliff like a white geometric beehive. You are in the caldera (volcanic crater), one of the world's truly breathtaking sights: a demilune of cliffs rising 1,100 feet, with the white clusters of the towns of Fira and Ia perched along the top. The bay, once the high center of the island, is 1,300 feet in some places, so deep that when boats dock in Santorini's shabby little port of Athinios, they do not drop anchor. The encircling cliffs are the ancient rim of a still-active volcano, and you are sailing east across its flooded caldera. On your right are the Burnt isles, the White isle, and other volcanic remnants, all lined up as if some outsize display in a geology museum. Hephaestus's subterranean fires smolder still—the volcano erupted in 198 BC, about 735, and there was an earthquake in 1956. Indeed, Santorini and its four neighboring islets are the fragmentary remains of a larger landmass that exploded about 1600 BC: the volcano's core blew sky high, and the sea rushed into the abyss to create the great bay, which measures 10 km by 7 km (6 mi by 4½ mi) and is 1,292 feet deep. The other pieces of the rim, which broke off in later eruptions, are Thirassia, where a few hundred people live, and deserted little Aspronissi ("White isle"). In the center of the bay, black and uninhabited, two cones, the Burnt Isles of Palea Kameni and Nea Kameni, appeared between 1573 and 1925. There has been too much speculation about the identification of Santorini with the mythical Atlantis, mentioned in Egyptian papyri and by Plato (who says it's in the Atlantic), but myths are hard to pin down. This is not true of old arguments about whether tidal waves from Santorini's cataclysmic explosion destroyed Minoan civilization on Crete, 113 km (70 mi) away. The latest carbon-dating evidence, which points to a few years before 1600 BC for the eruption, clearly indicates that the Minoans outlasted the eruption by a couple of hundred years, but most probably in a weakened state. In fact, the island still endures hardships: since antiquity, Santorini has depended on rain collected in cisterns for drinking and irrigating—the well water is often brackish—and the serious shortage is alleviated by the importation of water. However, the volcanic soil also yields riches: small, intense tomatoes with tough skins used for tomato paste (good restaurants here serve them); the famous Santorini fava beans, which have a light, fresh taste; barley; wheat; and white-skin eggplants.

It's no wonder that all roads lead to the fascinating and maddening metropolis of Athens. Lift your eyes 200 feet above the city to the Parthenon, its honey-color marble columns rising from a massive limestone base, and you behold architectural perfection that has not been surpassed in 2,500 years. But, today, this shrine of classical form dominates a 21st-century boomtown. To experience Athens—Athína in Greek—fully is to understand the essence of Greece: ancient monuments surviving in a sea of cement, startling beauty amid the squalor, tradition juxtaposed with modernity. Locals depend on humor and flexibility to deal with the chaos; you should do the same. The rewards are immense. Although Athens covers a huge area, the major landmarks of the ancient Greek, Roman, and Byzantine periods are close to the modern city center. You can easily walk from the Acropolis to many other key sites, taking time to browse in shops and relax in cafés and tavernas along the way. From many quarters of the city you can glimpse "the glory that was Greece" in the form of the Acropolis looming above the horizon, but only by actually climbing that rocky precipice can you feel the impact of the ancient settlement. The Acropolis and Filopappou, two craggy hills sitting side by side; the ancient Agora (marketplace); and Kerameikos, the first cemetery, form the core of ancient and Roman Athens. Along the Unification of Archaeological Sites promenade, you can follow stone-paved, tree-lined walkways from site to site, undisturbed by traffic. Cars have also been banned or reduced in other streets in the historical center. In the National Archaeological Museum, vast numbers of artifacts illustrate the many millennia of Greek civilization; smaller museums such as the Goulandris Museum of Cycladic Art Museum and the Byzantine and Christian Museum illuminate the history of particular regions or periods. Athens may seem like one huge city, but it is really a conglomeration of neighborhoods with distinctive characters. The Eastern influences that prevailed during the 400-year rule of the Ottoman Empire are still evident in Monastiraki, the bazaar area near the foot of the Acropolis. On the northern slope of the Acropolis, stroll through Plaka (if possible by moonlight), an area of tranquil streets lined with renovated mansions, to get the flavor of the 19th-century's gracious lifestyle. The narrow lanes of Anafiotika, a section of Plaka, thread past tiny churches and small, color-washed houses with wooden upper stories, recalling a Cycladic island village. In this maze of winding streets, vestiges of the older city are everywhere: crumbling stairways lined with festive tavernas; dank cellars filled with wine vats; occasionally a court or diminutive garden, enclosed within high walls and filled with magnolia trees and the flaming trumpet-shaped flowers of hibiscus bushes. Formerly run-down old quarters, such as Thission, Gazi and Psirri, popular nightlife areas filled with bars and mezedopoleia (similar to tapas bars), are now in the process of gentrification, although they still retain much of their original charm, as does the colorful produce and meat market on Athinas. The area around Syntagma Square, the tourist hub, and Omonia Square, the commercial heart of the city about 1 km (½ mi) northwest, is distinctly European, having been designed by the court architects of King Otho, a Bavarian, in the 19th century. The chic shops and bistros of ritzy Kolonaki nestle at the foot of Mt. Lycabettus, Athens's highest hill (909 feet). Each of Athens's outlying suburbs has a distinctive character: in the north is wealthy, tree-lined Kifissia, once a summer resort for aristocratic Athenians, and in the south and southeast lie Glyfada, Voula, and Vouliagmeni, with their sandy beaches, seaside bars, and lively summer nightlife. Just beyond the city's southern fringes is Piraeus, a bustling port city of waterside fish tavernas and Saronic Gulf views.

Oraia (beautiful) is the word Greeks use to describe Nafplion. The town's old section, on a peninsula jutting into the gulf of Argos, mixes Greek, Venetian, and Turkish architecture; narrow streets, often just broad flights of stone stairs, climb the slopes beneath the walls of Acronafplia. Tree-shaded plazas surround neoclassic buildings. The Palamidi fortress—an elegant display of Venetian might from the early 1700s—guards the town. Nafplion deserves at least a leisurely day of your undivided attention, and you may want to spend several days or a week here and use the city as the base from which to explore the many surrounding ancient sights.

Backed by imposing mountains, tiny Kotor lies hidden from the open sea, tucked into the deepest channel of the Bokor Kotorska (Kotor Bay), which is Europe's most southerly fjord. To many, this town is more charming than its sister UNESCO World Heritage Site, Dubrovnik, retaining more authenticity, but with fewer tourists and spared the war damage and subsequent rebuilding which has given Dubrovnik something of a Disney feel.Kotor's medieval Stari Grad (Old Town) is enclosed within well-preserved defensive walls built between the 9th and 18th centuries and is presided over by a proud hilltop fortress. Within the walls, a labyrinth of winding cobbled streets leads through a series of splendid paved piazzas, rimmed by centuries-old stone buildings. The squares are now haunted by strains from buskers but although many now house trendy cafés and chic boutiques, directions are still given medieval-style by reference to the town’s landmark churches.In the Middle Ages, as Serbia's chief port, Kotor was an important economic and cultural center with its own highly regarded schools of stonemasonry and iconography. From 1391 to 1420 it was an independent city-republic and later, it spent periods under Venetian, Austrian, and French rule, though it was undoubtedly the Venetians who left the strongest impression on the city's architecture. Since the breakup of Yugoslavia, some 70% of the stone buildings in the romantic Old Town have been snapped up by foreigners, mostly Brits and Russians. Porto Montenegro, a new marina designed to accommodate some of the world’s largest super yachts, opened in nearby Tivat in 2011, and along the bay are other charming seaside villages, all with better views of the bay than the vista from Kotor itself where the waterside is congested with cruise ships and yachts. Try sleepy Muo or the settlement of Prčanj in one direction around the bay, or Perast and the Roman mosaics of Risan in the other direction.

Off the coast of Croatia in the southern Adriatic Sea lie some thousand islands and the largest of them, Korçula, is considered the most beautiful. With an average of 3,000 hours of sunshine per annum, which guarantees a wide assortment of Mediterranean vegetation, it is not difficult to understand why seasoned travelers compare Korçula to a latter-day Eden. Separated from the mainland by a channel of only one mile, Korçula's main town, named the same as the island, ranks among the best preserved medieval towns in the Mediterranean. It is the island's main tourist, economic and cultural center. Thanks to its strategic location along the sea trade routes, Korçula has always attracted travelers and settlers. Korcula was founded by Greek colonists, who were followed by Illyrians, Romans and finally the Croats. The Korçula Statute of 1214 is one of the oldest legal documents to have been adopted in this part of Europe. The same century saw the birth of the famous world traveler, Marco Polo. The house said to be his birthplace can be seen in town. Korçulans have always been known as keen seafarers, excellent shipbuilders, stonemasons and artists. From their many voyages, sailors brought back new ideas, which eventually mixed with local customs. To this day, Korçula has maintained the tradition of performing knightly games such as the chivalrous Moreska dance, which has been in existence for more than 400 years. Visitors to Korçula enjoy its stunning location, natural beauty and medieval ambiance. And if that's not enough, the town offers numerous attractions that are within walking distance from the pier, including the City Museum and the Bishop's Treasury.

The Croatian island of Hvar bills itself as the "sunniest island in the Adriatic." Not only does it have the figures to back up this claim—an annual average of 2,724 hours of sunshine—but it also makes visitors a sporting proposition, offering them a money-back guarantee if there are seven consecutive days of snow (snow has been known to fall here; the last time being February 2012).

Venice is a city unlike any other. No matter how often you've seen it in photos and films, the real thing is more dreamlike than you could imagine. With canals where streets should be, water shimmers everywhere. The fabulous palaces and churches reflect centuries of history in what was a wealthy trading center between Europe and the Orient. Getting lost in the narrow alleyways is a quintessential part of exploring Venice, but at some point you'll almost surely end up in Piazza San Marco, where tourists and locals congregate for a coffee or an aperitif.