We arrive in port at Giardini Naxos at 10 am. We have an excursion set up for Taormina from 1:45-5:45. I would like to be able to go on into Taormina as soon as we get there, but don't know if that's do-able to catch up with our tour in Taormina. Or would it be better to plan to go back to the ship before hand? Or is there something to do in Giardini Naxos? Any help is appreciated!
Giardini-Naxos (Naxos, actually) has a good little museum and an important archeological site, if those things interest you. Taormina is small enough that you should have no problem catching up with your group there if you decide to do that. Find out what's on the excursion itinerary and do something else on your own. Just a stroll through the main street on your way to the Greek theatre (probably on your excursion itinerary) is a great way to spend some time. Excellent shopping in Taormina as well.