Hello.
I have been to Greece but not this particular area.
Quick Google type search with my laptop shows quite a few helpful links. August is several months away. Plenty of time to work things out.
Sample search below:
"Local transportation on Naxos is very regular, especially during the tourist season. There are plenty of places you can get to using the busses provided by the municipality, especially if your starting point is Naxos Town."
Good luck.
