We liked the stay in Paolo's apartment. It's 5 minutes walking from the port and the city beach, which is not that nice, but is okay if you want to take a quick dip. We really appreciated air-conditioning in the apartment as the weather was really hot at that time.
There was a really good cafe at the corner of the street - Agrillo Bar Pasticceria. We really liked their pastry and the service was really kind to us. Also, there are pretty good restaurants on the street Viale Antonio Gramsci, we liked Napoli 1820 most.
We had a great time exploring the surroundings of Naples - Lido Marechiaro (clean beach between the rocks), Spiaggia di Torregaveta (really nice beach, 1-hour away by train), one-day boat trip to the island Capri (really nice, crystal clear beaches). The city centre of Naples is not that nice, it's really dirty overall, but it was an interesting experience for us anyway. Thank you, Paolo, we enjoyed our stay here and recommend this apartment!