Sicily is not the most gay-friendly place in the world, but in Catania, Palermo and Taormina you could book any accommodation and will have a pleasant stay
Gays and lesbians should look for an accommodation in a town, in villages and small seaside resorts it could happen that they are not so welcome. Hotel staffs will of course treat you like any other guest, but the latter caused in the past here and then problems. In Palermo, Catania and especially Taormina you won't have problems at all, people are open-minded. In this category you'll find accommodations which say about themselves that they are gay-friendly, so if you want to be on the safe side, book one of these.