Giardini Di Naxos is a township at the base of the mountain on which Taormina is located. It looks quite interesting although we mainly passed through it numerous times on our way to and from Taormina.
However we did enjoy a wonderful meal in this family run restaurant on the beach front. I can recommend it.
A rather grand railway station serving both towns is nearby to the restaurant although the walk between the two is somewhat dangerous at several points where the footpaths disappear.