Alfredo is an amazing host- he made the most romantic house on earth, with windows - illuminators, antique furniture, covered in flowers in the most beautiful spot on earth. Yet it's very comfortable and has everything you would need in 10 days of vacation. I have traveled a lot around Italy and this has been the most amazing experience I ever had.
The house' only issue and still advantage is that it is situated high on the mountain and it takes time to get there on foot from the city. You have to walk for 15 minutes up the path, yet our 4 year made it easily up and down as there are small lizards and all kinds of flowers on the way so she was all the time excited.
I would recommend to take a car also to go around the island, as there are magic hidden places there, like roman termas or places for picnic with mind-blowing views, when you suddenly find yourself in the fog from the cloud passing by.