My husband and I stayed at Juliana's place at the beginning of October and had an amazing time. The apartment is in a great location tucked in a back street away from the hustle and bustle of the port, but a really quick walk to the water, the port, plenty of restaurants, cafes and bars, as well as the old town and castle. There is also a great beach in town, which is about a 10 minute walk from the apartment.
We were greeted by Juliana's father at the port and given an overview of the island and brief tour of the town, and some fresh fruit from his farm. We had sole use of the amazing terrace which had a nice view of the port (great at sunset) and sun beds. The apartment has air conditioning and we had a really comfortable 3 nights.
We would definitely recommend Juliana's apartment for your stay in Naxos.