I had a great stay at Windmill Naxos. George, the owner, was very friendly and offered a free ride to and from the port. The hotel was located some 10-15 minutes' walk from both the city centre and the beach, as well as restaurants, bakeries and shops. The houses look quite similar though, so it was a good thing that George picked me up from the port upon arrival. The room was spacious and clean and had a small balcony. All in all I had a very relaxing stay in Naxos.
I had a pleasant stay at Residencial S. Roque. The hostel is located a 10-minute walk from the city center and the bus station, and about 15 minutes from Praia da Rocha. You might want to go there first by a taxi, but after that it's quite easy to navigate around the city. My room was spacious and clean. The bathroom had a shower and a bathtub, and even a hairdryer. The complementary breakfast was basic but sufficient and good. The lady owner was particularly charming and helpful. Recommended.
The place is located only 5-minute walk from the old town. Near you have a minimarket and a bakery. I stayed in a single room with a toilet. The bathroom was next to my room; I was the only one using it. The room was quite clean and small but with enough hanging places for clothes. Unlike written in the description, the room had no fridge nor TV, but there were plenty of towels that were replaced often. The staff was helpful, but I always woke up after 7 to their talking and making breakfast.
The hostel is located a 10-minute walk uphill from Baščaršija. The owners speak understandable English and are ready to help, but it can be hard to get a hold of them. I booked a single room with an ensuite bathroom, but in reality I had to share the bathroom and toilet with another guest. The room and other facilities were clean and spacious. My room had a stove, tableware and running water, and I could use a fridge in the hall. All and all, a good stay. I would go there again.