There are just over a quarter of a million people residing on Corsica and a good percentage of those live in the two largest cities of Ajaccio and Bastia, which have international airports. Corsica is populated much less densly than its neighboring land masses, so a vacation should take into account the many nature reserves and wildlife areas, as well as the beaches of Corsica.
Ajaccio, Napoleon's hometown and Corsica's capital, is a good place to start your vacation. Head for the port, the old village, and the markets.
Corte is where the cultural fanatics will want to head; traditionally people on the islands of Corsica or Sardinia harbor a distrust of the sea and the invaders and pirates who use it, so the inland is where the "real" population has a chance to show its stuff. Above all, eat here, especially if you've come outside the high season, when wild game shows up on the table.
Folks who like the sea will appreciate the riviera-like Calvi for its seaside, if not its citadel. If you're going on to Sardinia, just 14 km away, you might head over to Bonifacio, with its spectacularly situated fortress.
Sartene was founded in the 16th century, and is the most typical of Corsican towns. Sartene is where you start if you're interested in Corsica's prehistory; the Musee Departemental de Prehistoire Corse is found in the town's old prison. 16 miles northwest of Sartene is Filitosa, the site of Corsica's biggest group of megalithic statues (open June-August).
The best source of inside information on Corsica on the net is William Keyser's ambitious Corsica Isula - Corsica from the inside.