If you get to Palermo (where the airport is), you can easily take trains to Agrigento (a must; 2 hours) and Messina (3 hours). Catania is a bit harder, a longer haul (5 hours). Taormina, another must, is 4:30. It’s hard to give you an itinerary because there are two Sicily’s —the coasts and inland. Inland you get villages so rugged and removed from notions of classic tourism that you might find yourself thinking you’re in Asia. The are many towns with spectacular Greek and Roman ruins. Siracusa has an island peninsula, Ortigia, which is breathtaking. You might consider renting a car in Palermo and driving south to Agrigento, then east to Taormina, to Catania, then Messina, and along the coast back to Palermo. You have two weeks. It’s perfectly feasible. I think Sicily better lends itself to car than train.