We were in Sicily two Januarys ago. Our first day on the island involved catching a late mid-morning ferry over to Medina which allowed us to make it to Taormina for lunch. Had plenty of time to see everything we wanted to and enjoy dinner, but could have stayed another day in that area. Taormina was breathtaking.

Stayed at the Sheraton Catania. Worked well for us. Next day did a day trip to Siracusa, which was also a day well spent. It was off season so many places (including museums) were closed, but still found plenty to do.

We had a 3rd day based in Catania and had ideas on another day trip - possibly to Piazza Armerina or Ragusa, but it was raining and my son and wife were sick, so we stayed close to the hotel. Did drive around Catania a bit.

From Catania we drove to Palermo with a stop in Cefalu. The town was empty, but it was another stormy day and the ocean had huge waves - allowing us the most amazing lunch right on the rocks with water crashing against the restaurant. Cefalu is definitely worth a visit if time allows.

From there drove into Palermo and stayed at the Hilton. Great location and stay. Enjoyed a couple days exploring Palermo.

In addition to what others have said to do in or from Palermo, will add that we spent a Sunday out in Castellammare del Golfo and enjoyed it. It was really cool with the picturesque beach yet snow capped mountains in the distance. There was a weekend market along the beach walk and we enjoyed a great late lunch at one of the seafood places as our last meal in Sicily/Italy.