We had a very enjoyable stay at Alexander's place, whose location right in the centre of Santorini is well served by 3 bus routes. So getting around the island by bus is not an issue.
Agni was most helpful at check-in and her recommendations about hikes and surrounding taverns were spot-on. The food was very good and moderately priced compared to other more touristic spots like Fira and Eia.
Finally, the feeling of living in a cave in an authentic surrounding makes it a memorable one.