Sicily offers such a wealth of sights and places to see that narrowing down your choices can be difficult. In order to optimize time, your best bet is to fly into one of the airports on the west coast (Palermo or Trapani) and leave from the one on the east coast (Catania) or vice versa; this allows you to see more without having to rush back to the airport at which you arrived.
Even when you've finally settled on an itinerary, you'll still have to travel a few hours a day getting from one place to another. The following itineraries aim to help you maximize your time in Sicily. Ideally designed for car travel, with no backtracking from one end of the island to the other, they are also suitable for bus or train, should you not have or not want a car.