One of our best Airbnb stays ever. It's just as the pictures describe (if not better) and Athena and Takis truly are super hosts. I would recommend this place to all of my friends.
A few quick notes: only one bedroom (medium-sized with double bed) is on the second floor (with a water view and en suite bathroom) but that's fine; in fact, we gather it's traditional to have more bedrooms partially sub-ground because they're cooler in the summer heat and still have windows that let in light. One bedroom in the lower level (the biggest bedroom with queen bed) has a HUGE bathroom and wonderful shower.
Note: The third bedroom that has one bunkbed and another twin bed does NOT have a door; it has a thick curtain you can pull closed. The other bedrooms have doors. We stayed in mid October and Naxos was quiet but there were still many restaurant options (Paradiso was great and very close to the house) and the weather really pleasant. One had the beach almost to oneself and you can walk for several kilometers looking out at the other islands. (BTW, we had a great time at the go cart place with our pre-teen daughter; it's between the house and Naxos city. Lastly, definitely rent a car. (VIP Cars works well for us.)