Siracusa
The home of Archimedes was the only ancient Greek city to rival Athens, and Sicily's most important locality until around AD 900. Ortygia, the oldest district of the city, is actually an island and has very charming medieval streets. Syracuse has some interesting sights rarely encountered elsewhere. The cathedral, for example, was built from an ancient Greek temple whose columns are visible along the nave. It's an insight into early Christian history, as this is how the earliest churches were constructed, literally converted from such temples. On a mythological note, the Spring of Arethusa is the place where the ancient Greeks believed that the beautiful nymph was taken to when she became a spring to escape an unwanted suitor.
Bottom Line: This charming city and its archeological site are a 'must see' if you're an ancient history buff.
Getting There: From Catania, take the SS114. Fastest routes from Taormina or Palermo are via Catania.
Dining: In the Ortigia district, Kalliope in Via del Consiglio Regionale 26 is rustic and charming. Another choice is Le Antiche Siracuse at Via Maestranza 2, which is also a small hotel (the restaurant is upstairs).