We absolutely loved our stay at Mary and Vincenzo's place. Firstly, they reacted within less than 30 minutes to our request via the airbnb site. The apartment is modern and clean and has a beautiful (huge!) terrace with stunning views over the bay. The cable car to the beach (€3 one way) is just across the road from the apartment. There you can rent pedalos, paddle boards and kayaks to explore the bays and their crystal clear waters.
Taormina is beautiful and has incredible views of Mount Etna (especially impressive from the Teatro Greco).
The food is of course delicious!
In short: Taormina is a must and Mary and Vicenzo's place is highly recommended! Worth every penny.