I would definitley recommend Alfredo's beautiful and sweetly decorated house near Lipari. Its a little cozy retreat, ideal for couples and you have plenty of space for your own. There a two big terraces from where you can enjoy the beautiful sunsets over the Aeolian Sea. And it is well equipped with really everything you need (except internet, but that was what we were looking for! :)) especially the hammock is great!

Alfredo was a really polite and helpful host, he picked us up at the harbour even late in the evening because our ferry was on delay.
He helped with everything, answerd quickly via sms and explained a lot. Thank you again!

According to the host, accomodation, furniture and cleanliness I would give 5 stars, it's just the location that missed the fifth:
You need a scooter, otherwise you can't reach anything without walking a few kilometers. And the house itself is located really rurally, where only a small dirtroad leads to it. But nevertheless it is totally worth it!

PS: One word according the scooter: Our experience with renting the scooter at Luigi's was not that positive, so we would personally recommend to choose one of the other renters. But maybe we had only some bad luck.