Taormina is an ancient Greek Theatre that has an amazing view of the surrounding area, which include medieval buildings, shops, bars, and restaurants
Agrigento is one of, if not, Sicily's most famous sites to see. There is eight temples that were thought to have been made between about 519 B.C. and 430 B.C. All of the temples were named after a Greek god.
The aeolian islands are a chain of small islands on the outskirts of Sicily that have great beaches, mud baths, myths and legends.
The Piazza Armerina holds some of the world's best preserved mosaics. So if you like art, this is the place to go!
Mt. Etna is a perfect 10,000 foot cone mountain. You can visit to the top of it all throughout the year. It fumes gently throughout the year and some may be lucky enough to see it go off, being the most active volcano in Europe.
Syracuse is a city in Sicily that is essential to your travel there. It has a lot of history, some including the archaeological sites and architectural buildings and design. There is a very famous theatre and the catacombs of San Giovanni.
Cava Grande is a natural reserve that is well kept by Sicily, it is considered a secret because it is so hard to find. There are waterfalls and water ponds that can also be visited.
Palermo is the regional capital of Sicily.
Catania is the second largest city is Sicily, there are quite a few piazzas and the Duomo is most people's favorite.
Acireale isn't famous for history or architecture, it is mainly famous for its carnival. I recommend going for that!