Park yourself in either Palermo or Catania and spend 3 days exploring the main city. Dedicate 2 days to side trips – one to Taormina and one to Mt. Etna.
One Week
Explore the eastern coast. Start with 3 days in Catania, followed by a day each in Taormina, Mt. Etna, Siracusa, and Ortygia Island.
Two Weeks
You can see most of the island in two weeks. Add to the above itinerary 3 days in Palermo, 1 day each visiting Trapani and Erice and another day seeing one of the towns along the coast. End in Agrigento.