Funny you should ask as I just returned from Sicily on Sunday. There is much to do in Sicily and it all depends on your interests. I really enjoyed visiting the Greek Theatre in Taormina. We also took a trip up Mt. Etna and that was fascinating. If you like Greek and Roman history then Sicily has much to offer. Siracusa has a wonderful Roman and Greek Theatre that sit right next to one another. The Valley of the Temples in Agrigento is also a wonderful spot to visit for Greek Temples.
There are also some great beaches in Sicily including San Lorenzo, Pozzallo, and Sampieri. My favorite place that we stayed was a place called B&B Quartarella which is located in Modica. Absolutely beautiful.