The best time to visit Sicily is between May and July, when the weather is warm, but not hot. Joel and I visited Taormina in mid-May and could not have been more impressed. To get to Taormina, we flew into the Catania (CTA) airport, took a bus into the city, and then a train from the Catania Centrale station to Taormina-Giardina. From there, you must take a taxi into the main part of Taormina. You can find the timetables and prices here, and buy your tickets online, then use your phone to present your tickets to train operators.