Downtown Athens is an unlikely combination of the squalid and the grand: the cavernous, chaotic Central Market, which replaced the bazaar in Monastiraki when it burned down in 1885, is 10 minutes from the elegant, neoclassic Old University complex. The surrounding area is filled with the remains of the 19th-century mansions that once made Athens world renowned as a charming city. Some of these are crumbling into the streets; others, like the exquisite mansion that has been converted into the Numismatic Museum (once the grand abode of Heinrich Schliemann, discoverer of Troy) have regained their lost loveliness. Such buildings rub shoulders with incense-scented, 12th-century Byzantine churches as well as some of the city's most hideous 1970s apartment blocks. The mix has become headier as artists and fashionistas have moved to the neighborhoods of Kerameikos, Metaxourgeio, and Gazi and transformed long-neglected warehouses into galleries, nightclubs, and ultrachic restaurants.

A good 10 blocks directly north of the Old University complex, the glory that was Athens continues at the city's legendary National Archaeological Museum. One of the most exciting collections of Greek antiquities in the world, this is a must-do for any travelers to Athens, nay, Greece. Here are the sensational finds made by Heinrich Schliemann, father of modern archaeology, in the course of his excavations of the royal tombs on the Homeric site of Mycenae in the 1870s. Here, too, are world-famous bronzes such as the Jockey of Artemision and a bronze of Poseidon throwing a trident (or is it Zeus hurling a thunderbolt?). An added treat is the neighborhood the museum presides over: Exarchia, a bohemian, free-spirited (though nowadays a bit rundown) district that is mentioned in hundreds of Greek folk songs and novels. The area evokes strong feelings in every Athenian for here, in 1973, the students of Athens Polytechnic rose up in protest against Greece's hated military dictatorship. The colonels crushed the uprising and tanks killed many students, but the protests led to the junta's fall the following year. Today, students, intellectuals, and anarchists often fill its many cafés and tavernas, debating the latest in domestic and global affairs. Recent reverberations shook the area when rioting of an unprecedented scale shook the city center in December 2008 after clashes between the Athenian police and local youths, provoked after a police officer fatally shot 15-year-old Alexander Grigoropoulos. Today, things have pretty much returned to normal (though it is advisable not to visit the area on November 17th, the annual anniversary of the 1973 Polytechneion uprising).