There are a few things to know about traveling to Sicily. One, you should really budget a good two weeks if you really expect to take in everything the island has to offer. Two, a tour of Sicily is primarily a tour of its coastal areas; although there are some terrific inland locales to visit, the ultimate Sicilian vacation would take you all the way around its circumference.
The jumping-off point would be the exotic, chaotic capital city of Palermo (since this is where the airport is), after which you could head west to Trapani and Marsala (see below) or, more likely, east to Cefalu, Messina, Taormina, and Siracusa. If you have the time, try to budget a day or two on the Aeolian island of Salina (where "Il Postino" was filmed), where the caper berries are as big as grapes and the seafood is among the best you'll ever eat.
Here are but a few tips for the major Sicilian cities:
Palermo feels like an exotic capital city, as it is a major port town with gorgeous food markets, especially la Vucciria market, down toward the la cala harbor. A Moorish influence is evident in both the architecture and the food of Palermo, so the restaurants have a very different feel here than even the rest of Sicilia. I love the mysterious garden feel of ai Mandarini, where produce is treated as regally as the stunning seafood. At just 30 seats, Osteria dei Vespri, right off of Piazza Croce, is as tiny as it is delicious. They're working with pure tradition here, and it feels that the Corleone family could walk in any moment. Il Ristorantino, despite its diminutive name, is anything but small. They serve excellent fish and creative antipasti in a quiet residential setting that you might have otherwise passed by. Do not miss Santandrea, just off the piazzetta of the same name, steps away from the Vucciria market. Their wine list is among the best in Sicily, and this would be the place to have your first taste of pasta con le sarde and understand the hullabaloo about something so perfect, so poetic, so right...
25 kilometers out of town, in Villafrati is a place that certainly merits the voyage called il Mulinazzo. Let the chef rip on a tasting menu (degustazione), as it will be worth the entire trip, and a return...
If you choose to go west, up around the horn to the Northwest coast is Trapani, mostly known for its sea salt and access to the ferry boats that will take you to the paradise islands of Lampedusa and Pantelleria. The food is simple in both Trapani and the islands, but the language becomes an issue in all three places. I myself have had serious difficulty understanding both the accent and the dialect in these areas, so be prepared. Heading east, in the Garden of Eden City of Taormina, I love al Duomo, where you can dig on magnificent traditional seafood in a 35-seat restaurant where everyone knows each other (and each others' business)… Another great one of equally diminutive stature is called Maffei's (I know, I know, the "apostrophe-s" is killing me too...). Both al Duomo and Maffaei's are paragons of traditional Sicilian fare, and will not disappoint. New to the restaurant scene is Nautilus, a place that I found very intriguing, despite the ubiquity of Spanish-inspired foam sauce. There is a large wine list with some international touches, and a very serious kitchen, one that merits attention on a long trip, but is probably less essential if you're only here for a few days.
In Siracusa, I have always loved the restaurant Jonico for its spectacular waterside location. The food is simple and very much a part of the southern Italian tradition of large, high-end seafood restaurants. This one serves pizza as well, and has a discreet selection of Sicilian labels on the wine list. For a few less euros, L'arlecchino, does the same thing in a more traveled and hip part of town. The last time I was in Siracusa, I had a great meal at a place called la Medusa, where we ate the traditional antipasti, followed by a cuscusu with shellfish that was incredibly light and more intelligent than any risotto in recent or ancient memory. The owner is Tunisian, so it all made sense then. I can't guarantee that the owner nor the quality are the same, but sometimes in Sicily you have to roll the dice.