We stayed here on our honeymoon and loved it. It is a small family-run set of luxury suites. Iannis and Maria are very welcoming and attentive, so it feels very personal. Not a traditional hotel. Iannis welcomed us with a talk about things to do on Naxos, along with a bottle of ouzo, cheese, sardines, and other treats. They cooked us a large and very tasty dinner. Iannis has an impressive wine cellar, so you should definitely have him pick you out a bottle.
It's not located right on the beach, so you will need a car, but you'll want one anyway to explore the island.
We stayed in the Junior Suite. The room is well stocked with a mini fridge, glasses, bottle openers, etc. Our room had a private balcony with a nice view and a shared swimming pool. The rooms are a good size, very clean, and nicely appointed. The bathroom has a jacuzzi tub, but it is a bit on the small side. Definitely too small for two people and even a little cramped for one 6 foot tall man. Also, it doesn't have a traditional shower, just a detachable shower head that can be held in your hand to wash yourself, but we ended up flooding the floor every time because the tub is so small. It looked like the larger suites had private outdoor showers and maybe a larger tub, so it is probably worth it to consider them.
Naxos is well worth a visit for those looking for something other than the standard Santorini/Mykonos package deal.