Antonio's flat is in a good location, 200 meters away from the sea. The district itself is not really interesting, but just next to it you can go diner and have a drink in the district of Chaia.
However, the noise can be disturbing, because the street is very frequented by traffic. But i don't think there is really a quiet district in Napoli's center.
Be aware too, there is no WiFi in the flat, and the bed is quite bad.