I think that was set on Salina which is another of the group of islands (the Aeloian Islands). However, the film called 'Stromboli' was filmed on Stromboli in the 50s. It starred Roberto Rossellini and Ingrid Bergman and we did actually visit the house in the film. It is rumoured that they had an affair whilst making the film.
Slightly off topic, but a few years ago we had an idyliic holiday on a small island off the coast of Sicily called Lipari.
It's one of a group of islands in that area and one day we went on a boat trip to a neighouring island called Stromboli. It's a night time trip because the volcano on Stromboli is constantly active and it's a wonderful sight by night.
People live there quite happily but it does have a warning siren system if the thing looks like it's going to get out of control.
Bit too hit and miss, if you were to seriously consider this.
Too dependent on wind direction and thermals.
When I went up in a balloon, the in-flight service was phenomenal. The landing wasn't too comfortable though