All over Sicily are these beautiful mountain towns. My father is from one, Gangi, and it, along with dozens of other towns, are so picturesque it's unbelievable. I enjoy driving to the very tops of these towns and finding the top square, or the main church. Then do some people watching, grab a gelato, walk the thin cobblestone streets. You can visit Sperlinga Castle, which, I have never seen more than 3 people there at a time. Cefalu is touristy, but my god, the whole town is like a museum, it's so cool. From your drive between Palermo and Torrenova, work your way into the middle of the island. You'll find plenty of cool places. Be careful on the mountain roads, they are thin and high. Take your time and enjoy the scenery. Pick some cactus pears from the side of pretty much any road, but wear some gloves or bring some tweezers for the needles. You'll be sure to fall in love with Sicily.
I would say have a car. If you are staying on the eastern part of the island. Definitely see Catania and Etna. Siracusa (Ortygia). Taormina, the Val da Noto around Ragusa, Modica etc. the baroque churches are amazing. The western part of the island is a whole other trip.
See this film I made it.