We had a magical stay in Cinzia's house. I can't recommend it highly enough. We didn't have a car but that doesn't matter (it takes only 10 minutes to walk to Castelmola on foot via a short cut, then you can either take a bus to Taormina or also walk another stunning 20 mins down the steps).
Cinzia came to pick us up from the centre and showed us where to find everything. The house itself has a massive terrace and a massive bedroom balcony that overlooks Castlemola, Taormina and the shore, it's truly breathtaking. It was extremely clean and well-maintained, and had everything we needed including some basic food supplies and water. Plenty of towels, 2 double beds, a comfortable sofa plus outdoor lounges and dining table to take in the view. Cinzia was constantly available on Whatsapp and helped us with travel arrangements for our journey home. We even got to know the neighbour Angela, who gave us some fruit from her grounds.
Also highly recommend Le mimose restaurant in Castlemola - lovely family restaurant that's off the beaten track and serves fresh fish and generous portions.
Highly recommended, especially if you like being a little further away from the tourist trails but still close enough to get to on foot.