We had a good time in Lipari resp. on the Aeolian Islands (September).
From Claudio's apt. you have a beautiful panoramic view across Lipari and the Lipari Bay. And a spangled sky by night. There is a lot of space in and around the apt.and nice pool, too.
Since the location is a little bit remote in the hills you may want to consider in advance how to move around comfortably. But no worries, your aren't lost (Bus, shuttle by our hosts etc.)
If there are any questions Claudio and/or your local host Paolo respond in no time and provide support.
All in all: Our stay in Claudio's place was really enjoyable - and recommendable.