Which areas are suggested if you are spending 6-7 days?
Our favorites were Taormina, Agrigento with its beautiful Valley of the Temples, Segesta, Erice, Selinunte, and the spectacular Villa Romana del Casale near the town of Piazza Armerina.
Taormina is heavily visited but without a doubt the prettiest town in Sicily. It makes a good starting point and you can easily spend 2-3 days there.
Stay at B&B's if you possibly can - you'll get a wonderful feel for Sicilian life and people.