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.

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.

Malta's capital, the minicity of Valletta, has ornate palaces and museums protected by massive fortifications of honey-color limestone. Houses along the narrow streets have overhanging wooden balconies for people-watching from indoors. Generations ago they gave housebound women a window on the world of the street. The main entrance to town is through the City Gate (where all bus routes end), which leads onto Triq Repubblika (Republic Street), the spine of the grid-pattern city and the main shopping street. Triq Mercante (Merchant Street) parallels Repubblika to the east and is also good for strolling. From these two streets, cross streets descend toward the water; some are stepped. Valletta's compactness makes it ideal to explore on foot. City Gate and the upper part of Valletta are experiencing vast redevelopment that includes a new Parliament Building and open-air performance venue. The complex, completed mid-2013, has numerous pedestrian detours in place along with building noise and dust. Before setting out along Republic Street, stop at the tourist information office on Merchant Street for maps and brochures.

Trapani, the most important town on Sicily’s west coast, lies below the headland of Mount Erice and offers stunning views of the Egadi Islands on a clear day. Trapani’s Old District occupies a scimitarshaped promontory between the open sea on the north and the salt marshes to the south. The ancient industry of extracting salt from the marshes has recently been revived, and it is documented in the Museo delle Saline. In addition to the salt marshes,Trapani’s other interesting environs include the beautiful little hill town of Erice, the promontory of Capo San Vito stretching north beyond the splendid headland of Monte Cofano, the lovely island of Motya and the town of Marsala. Trips farther afield will take you to the magnificent site of Segesta or the Egadi Islands, reached by boat or hydrofoil from Trapani Port.

Known in Sardinia as Casteddu, the island's capital has steep streets and impressive Italianate architecture, from modern to medieval. This city of nearly 160,000 people is characterized by a busy commercial center and waterfront with broad avenues and arched arcades, as well as by the typically narrow streets of the old hilltop citadel (called, simply, “Castello”). The Museo Archeologico makes a good starting point to a visit. The imposing Bastione di Saint Remy and Mercato di San Benedetto (one of the best fish markets in Italy) are both musts.

Italy's vibrant capital lives in the present, but no other city on earth evokes its past so powerfully. For over 2,500 years, emperors, popes, artists, and common citizens have left their mark here. Archaeological remains from ancient Rome, art-stuffed churches, and the treasures of Vatican City vie for your attention, but Rome is also a wonderful place to practice the Italian-perfected il dolce far niente, the sweet art of idleness. Your most memorable experiences may include sitting at a caffè in the Campo de' Fiori or strolling in a beguiling piazza.