We decided to base ourselves in Giardini Naxos to explore the surrounding areas, including Taormina which was 20mins up the road (by car). We had a brilliant stay at Alessandro's. Uninterrupted views of the sea with the sun rising every morning from the balcony. We could also see to the left Taormina and watch the world of Giardini Naxos go by.
The apartment was spacious, the photos don't do it justice! Everything was clean and tidy. It was up 3 flights of stairs, but then again you do have the amazing view. Downstairs was a bar but we didn't hear a peep mainly because of the soundproofed doors. We were there during low season and had no issues parking the car. There might be a little more difficulty in the high season but I suspect that's the case throughout Sicily.
I highly recommend staying here. Alessandro was helpful, checked in with us to make sure we were all ok and made recommendations. We were sad to leave and would certainly stay again.