From May 5 to 7, 2014, a friend and I stayed in Taormina at Casa Cuseni: http://www.casacuseni.com/en/. This is a villa with lovely grounds, built in 1905, that has been converted into a B&B. Taormina is perched on a hillside, and this house is located "above" the main town; this means phenomenal views from your terrace. It also means climbing back up from town to get back to your room, but we felt it was worth the tradeoff. My friend and I had separate rooms and shared a hall bathroom (the rooms with private bath were beyond our budget).
We had looked at a less expensive place, the Hotel Splendid. But reading the reviews, it seemed merely OK, and it wasn't cheap (something like €80 per night for a single). So, we decided to splurge on Casa Cuseni: €130 each per night, plus €15 per night for parking. That is, by far, the most I've ever paid for a bathroom down the hall.
However, Taormina is magic, and the lovely grounds and atmosphere of this place were special. The rooms (I had the Bertrand Russell room and my friend had the Greta Garbo room) were quite large. WiFi was not only included, but strong. Salvatore is the concierge during the day, and he gave us great restaurant recommendations and other assistance.
I'd certainly stay here again. However, it is not suitable for anyone with any mobility impairment, as you not only have to climb up from town, but you have to climb from the main gate to the house, then climb stairs to your room, and climb a further flight to the breakfast room. Of course, if this is an issue, all of Taormina will be a challenge; the main drag is relatively level, but everything else in town is either up or down from there. Also, while you can get to Casa Cuseni without driving into Taormina's ZTL, our Garmin GPS tried to take us via the ZTL. Luckily, I saw the sign in time, and at the nearby parking lot (parcheggio Lumbi) we were able to get directions.