Great suggestions so far. Would agree that the southern coast is a beautiful drive and if you do it you could spend a day or two in Trapani on the west coast, a beautiful seaside town. A half-day side trip from there would be to take the funicular at the edge of Trapani up to the mountaintop town of Erice. Have to admit I was a bit scared in the cable car since you're going straight up - 750 meters in 10 minutes - but it was worth it for the views and walking around town.
On the way to Palermo - or as a side trip from Palermo - you could visit the temples at Segesta. Another side trip from Palermo would be to visit Cefalu, further east on the coast from Palermo, a
beautiful little beach town on the end of a point.