Even though we had a bit of trouble finding the house on the first day, once we did it was a lovely surprise, it has a beautiful view and you really feel like you have arrived in Stromboli. It's really close to the main square and to the port (we took the wrong turn on the first day) and to amenities such as shops and restaurants.
When we were there they had no internet so we went to a restaurant around the corner called Luciano's, with friendly staff and nice food too. There are also some neighborhood cats who come and visit quite often so I recommend that you leave all food out of reach whenever you're not in the house or you're sleeping, since the kitchen is outdoors you might find they scavenged all your arancini when you wake up!
The communication with Gianpaolo was great, as he lives in Catania he can give you good tips on how to get to Stromboli from other islands and he helped us a lot when we were on our way there. Signora Rita, who welcomed us there, was very nice and helpful, even though she doesn't speak much English so if you need anything while on the island you might need to make an effort to communicate.
In general it was a dreamy stay and we would definitely go back. Thanks Gianpaolo and thanks Signora Rita :)