It's called Villa Paradiso for a reason. The photos don't even do justice for the view from the common terrace, it's just beyond beautiful. I loved staying in this little apartment, there was everything one could need for a short stay, and the private little terrace was also wonderful. Claudio is an amazing host!
I would probably recommend asking for his help to rent a scooter / car / e-bike, but it's also possible to walk and use the public transport to get around, to go to Lipari town and back. However, be aware that there are no buses in the evening, and the roads can be very steep, so walking is definitely an exercise!
I loved everything about it and will be back.