We went to Taormina a few years ago from the mainland. We took the train which crossed the strait by ferry. It's very interesting how they do this. The whole train goes on the ferry, takes a little while to get everything on and ended up in Catania, I think, where a taxi took us to Taormina to our hotel. Once in Taormina, we rented a car. The manager of the rental company was very sweet and kept reminding us to keep our purses with us at all times..not in back...make sure you show no suitcases, etc. He was like a parent of teenagers. We drove all the way down south to a town called Pachino and back. Very nice ride. We also made another trip a couple of years later to only Sicily. We started in Palermo and took the train with stops around the island but picked up a rental car in Ortigia near Siracusa as we wanted to be more flexible. Had a great time and we will be going back next year. Sicily is great and the people are very kind and sweet.
Have a great trip.
Mary