We ended up at Andrea's for dinner on the very first night in Taormina. The food is amazing, very tasty and the staff is quite nice. I had the antipasto di mare which I rank top among all of them I ever had. The Caponata is also very good. Andrea is very welcoming and will stop by your table a couple of times to check that everything is going great, which was definitely the case for us. At the end we went back 3 more times (in 1 week) for pizza and other types of food as we found the place conveniently located, with a good atmosphere and reasonably priced (Taormina is very expensive and this restaurant is priced in line with the other places around it - i.e. is not cheap, is just not as expensive as others).
A special thanks to all the staff there and to Andrea, who offered us a few glasses of limoncello at the end of our holidays. Will definitely go back next time I am around.