We had a very good stay in Konstantinos' place. We stay with our 3 kids, the appartment was clean and confortable. A bit small but ideally located (literraly 20m away from the beach and restaurants). Agios Prokopios is quite animated with a very good restaurants and beautiful beach. It's good place to be based if you want to visit Naxos (I really recommend to not stay only in Ag Prokopios, you would miss the real flavour of Naxos) and it's more calm than naxos town (perfect for the kids).
Despite location just in front of restaurant and the street behind main street, the appartment remains calm.