There are plenty of things to do in Sicily and there are a few beach resorts on the northern shore of Sicily but are a few in the town of Torre Colonna Sperone which is just south of Bagheria and the towns of Mondello and Capaci which are both just west of Palermo. There is really only one sizable area on the southern coast of Sicily that has any beach resorts and that is a little east of the town of Rocca San Nicola. There is also areas all along the coast that has usable beaches but it isn't developed as a resort and is mostly used by the local residents.
Since you may not be in Sicily for the beaches there are plenty of other things to do everywhere. You would think that Sicily being as far south as Italy can get that it wouldn't be a big ski area but it is with over 75 ski resorts scattered throughout the island making skiing accessible almost everywhere. With the average low temperature in Sicily in the winter being in the mid 40's fahrenheit you could spend the day on the mountain slopes where it is much colder skiing and spend the evening waking around town with a light jacket on.
If you are interested in archeological sites Sicily has many to offer with not only ancient Roman sites but Greek sites as well. One of the most famous and also a world heritage site is near the town of Syracuse which was founded in the early 700s BC. Some of the more popular of the ruins there are the tomb of Archimedes who was famous ancient scientist, a Greek Theater built in the 5th century and a stone quarry with some interesting caves.
Agrigento also a famous area for ancient ruins and also home of the world heritage site the Valley of the Temples. The valley consists of temples some Christian catacombs and an area of gardens.