If you're looking for a quiet place at a supreme location, you have found it! Liparo is great to enjoy the beautiful sea and the surrounding nature.
We stayed there in October, and most of the time we were all alone in the bay. The water of the sea was crystal clear and we enjoyed swimming and snorkeling every day. The only downside was that many restaurants were already closed so we had to drive quite a bit to dine.
Eleftheria is a great host and always happy to help.