The apartment is small but perfect for its purpose. Very clean, with excellent aircon, but does suffer from noise at night from the road that routes one way traffic heading for the town centre inches past your front door. If you are familiar with Italian driving you know what to expect. This eases off over night but the occasional scooter with loud exhaust or truck can wake you. A pair of ear plugs may be a solution.
The view from the small balcony makes for an enjoyable breakfast. Other than that we ate out every evening. We had great local food - use tripadvisor to select the restaurants, although the majority have good reviews. You are paying higher prices just due to the fact it is Taormina, and it is a bit of a tourist trap.
We had one opera evening at the Teatro Antico, which was awesome. The setting is amazing, followed up by fireworks. Highly recommended.
The cable car to the beach provides a good service. It is typical Italian Rivera, probably unchanged since the 60's. Very ordered sun beds with parasols arranged in linear fashion, but very quaint all the same. typical cost is €20 per pair of beds plus parasol. I think the Isolla Bella is the best, or most picturesque beach, with good swimming and snorkelling, however note that the beaches are pebble and shingle.
We rented a hire car for a few days, from Hertz in the town. $80 for a day approx, €140 for three days - we took the longer options to save the trauma of the bus journey back to the airport, which stops frequently and adds probably 45mins to the journey (Taormina to Airport in the hire car takes approx 50mins to 1 hour). Word of warning - despite the ordered sunbeds, most other aspects of Italian infrastructure is reasonable chaotic. The airport was chaos when we arrived, so arrive earlier than you would normally and be prepared to queue.
The hire car is also great for visiting Etna - saves on the expensive excursions. The roads are good (as they have to handle a steady stream of coach traffic), but be prepared for hairpin after hairpin as you climb through the lava fields to the base station. We then took the cable car up to approx 500m from the active crater. 4WD's can then take you the rest of the way, but it starts to get expensive, (base station to crater will cost in the region of €80 each I suspect). Still - its a good experience and worth the treat if you like a bit of scenery, geology, views and heights etc. If you want to head to the top be prepared with some rugged shoes/boots and a few layers of clothing - its gets pretty chilly up the top, and actually promotes skiing during the winter.
All in all we liked the apartment, liked Taormina (probably prefer the Amalfi coast), loved the food and the theatre.