This was my dream vacation and I cannot wait to return. The house is above an unspoiled, private swimming cove with stairs spiraling to the water so there is no reason ever to leave the house if you want only to swim and relax. If you do choose to explore, there are small beaches to the South, hiking out the door and the charming towns of Aperanthos, Filoti and Chalki in driving distance. Walk to dinner by the sea in town or drive a bit farther South to the more upscale Ostia Inn. We hiked from the house to Aperanthos (twice), had lunch and returned. If you are of a hiking persuasion, Mt. Zas has a beautiful view.
You will need a car to grocery shop in Naxos town. There is no public transportation on this part of the Island (and few tourists). Dimitri can tell you the best supermarket. The drive from Naxos takes about an hour so you probably won't want to shop every day. The drive is stunning, though and each town along the way is worth exploring. The 12 minute drive down from Aperanthos is steep and switch-backed but lightly trafficked (no buses) and drivers are generally courteous. A mile of dirt road to the property.
The house was super clean. Everthing worked perfectly. We were early in the season so the garden was just beginning, but it was beautiful.