In October, you can request permission to park at the restaurant, including for nighttime parking.
There is a nice and quiet parking area available on private property. To park, you need to ask permission from the friendly restaurant owner, who is also a camper. It is highly recommended to try the seafood dishes, especially the "fregola alla pescatora."
We spent a night in the restaurant's private parking lot with permission. There is no shade, but it's a good spot for a walk to the tower and the busy beach. Dinner at the restaurant costs between €30-€36 and is very good. The manager is friendly.