We were made very welcome by Francesco, who owns the apartment and lives downstairs. The area was lovely, in a historical part of the town. The street down below is busy with cars, but being on the fourth floor meant that we couldn't hear them (there's no lift, though). The most lovely thing about the apartment is that it has two balconies: one at the front, overlooking the sea; and one at the back with a view of lush woodland. It was idyllic really. The beach is 30 seconds away and there are supermarkets nearby for supplies. There is also a bus stop right outside, convenient for Catania and the airport, and also Taormina (which is 15 minutes away by bus).
I highly recommend this studio apartment for a stay in Giardini Naxos.