Antonis' place is highly recommended. The apartment is even better than on the pictures. One floor up, and because the street is already a bit higher you have a very nice view over the city and sea from the balcony at the entrance.
Very clean, quiet, 2 minutes walking from the restaurants and shops.
Antonis is also very helpful: picked me up from the port and made recommendations on what to see on the island.
Perfect spot: the city of Tinos is very nice and the nature is stunning on the Island!