In Naxos a place called Tony’s and in Milo’s I’m not sure of the name but it was just behind the little bakery and kebab shop at the front by a bridge if that helps lol
book far in advance!! you can get decently priced accommodation on most greek islands but you have to get there quick because there are sooo many american and australian tourists trying to do the same thing. I did return flights from athens with ryanair which was quite cheap, unfortunately some of the longer ferries are quite expensive though