My cousin and I had a very nice stay at Nostos Studios. We were welcomed very warmly by the host and found our room to be all we needed, it is well equipped and spotlessly clean. The apartments are close to the town beach and the old town, like 5 - 10 minutes walking distance. There is a nice little square with some cafes nearby.
Naxos is a very lively town, so if you are looking for shops, many restaurants and a lively beach that this is the right spot for you. If you are looking for more remote areas you can always catch a bus from the town center.