Evelyn, Laura has some great ideas for you! I will not go to Sicily without 1st consulting, and then taking my Lonely Planet guidebook. Also post your question on the Tripadvisor site....and plase tell us how much time you have avail for your trip. (There are some very knowledgeable people on TA.)
We have been twice, and absolutely love Sicily! Do some reading and plan your trip. We stayed in three Agris in Sicily, and loved each one. One was a RS pic in the Madronie Mtns (Il Vecchio Frantoio...fantastic), one was a Karen Brown recc near Syracusa (Il Limonento, rustic, great hosts!), and one was near Pacheo (Baglio Costa di Mandorla, cheap, with a pool, NE Italy). We also loved staying in the Aeolian Islands on Lipari.......Diana Browns B@B was absolutly fun and central.
Be careful if you plan on staying in Palermo.....the crime at night is a problem in some areas, and driving in Palermo and Catania is NOT for the faint of heart!
Send me a personal message for more info.