Taormina gets big play, and it's a great town, but we'd like to make the case for Siracusa. Ancient Syracuse was the most important city in Greek Sicily and a rival to Athens.
Both of these fabulous towns are appealing - Taormina on top of a mountain and Siracusa along the sea. Ortygia, Siracusa's most popular historical district, is largely closed to traffic, like Taormina, and consists of charming, winding streets. Apart from an important archeological site and museum, and Sicily's only remaining Caravaggio, Siracusa offers great restaurants and shops, while Syracuse Cathedral (originally a Greek temple) and its mikveh are among the oldest structures of their kind in Europe, representing two important faiths - three if you count mythology.
Siracusa is a great "intellectual" alternative to Taormina's crowds. We like to think that Hemingway would have preferred it as his favorite Sicilian city.