I've done a fair bit of travelling, and Sicily is my favourite place. Been around the island last summer, and have gone back a couple times since. As el says, skip Palermo and drive west. He's right about Zingaro, beautiful place, and the archeological sites on the island are incredible. Segesta is one that's close to Palermo/Trapani/Castelamare, and right around the bend there is an agriturismo that you can sleep and/or eat at, and which to me is the most relaxing place in the world: Pispisa. They don't speak English, but the food is great and you can just lounge about or walk around the hills overlooking Segesta. It's well positioned for the north west part of the island.
I could write many pages, but should do a bit of work instead. Just one more thing:
I'm a bit weird, but for me Poggioreale Vecchio was one of the most memorable sights — it's a town which was abandoned after an earthquake a few decades ago. It's worth ignoring the no trespassing signs, totally surreal.