We just love the Island- 2 years ago, DH and I flew to CAtania then drove up past Taormina, where we had lunch and a stroll, then up and around to the West, and stayed in a lovely Hôtel near wonderful, Norman, Cefalu for a few days, then on to the far Western tip and visited that whole area, and then back to Cefalu for a few days, and down cross country back to Catania, making stops at old Byzantine sites.
Last year we went with sil and bil from UK- again flew to Catania, then a few days in wonderul Ortigia, the small historic peninsula off Syracuse, then rented a villa in the countryside near Sampieri (where the old derelict factory is- we often see in Montalbano) and visited all the baroque towns, Noto, Ragusa, Modica, Scicli and of course Punta Secca, where he 'lives' (Marinello/Vigata in the book), and then along the coast to stay for a few days in AGrigento, and visit the valley of the Temples, and further along to walk in the countryside and see the amazing flowers.
This year, as said, joining them again, but will stay just one week in the Taormina area and not do as much travelling.
So fire away for advice- First question, will you be hiring a car and travel- or want to go and stay in one area, without a car, and go on a few guided tours. Just depends. Both Syracuse and Taormina are easily reached from Catania airport by train or bus or even Hôtel transfer. If you intend to go to Taormina, ask me again when we return- and I'll know more about it by then- and tell yu about our Hôtel and transfers, etc. Just depends what you want. Taormina has 2 parts, the historic town, up the hill, and the beach resort, along the coast below.