Few years back we stayed in Cefalu on the north coast. Easy to explore with a train line into Palermo and along to the islands off the north coast. Hired a car and drove into the interior and out to the west coast. Loads of history, culture, wine and sunshine.
If you go and you are in the right part (Cefalu or nearby) don't miss the opportunity to walk up Stromboli (active volcano) as the sun sets. You'll need a guide and accommodation for the island and you get up to the top near midnight. Guide leads you down and you'll see why he or she was needed when you go back on the ferry the next morning.
Added: when we went, the hike up must have been a bit later than on those pics, as the sun was setting when you turned a corner and saw the glowing stream of red lava going down into the sea. Then at the top it was pitch black and you were just looking down into the crater bubbling.
NB. Watch your gear on public transport. I have no pics from that trip as my old school much-loved Nikon was nicked off a train on the way to Palermo.