We loved everything about our stay at Kostas' place. Kostas was great - he arranged for us to be picked up from the airport and met us the first night to give us an overview of the island as well as give us some ideas of things to do in the bad weather. He also took us to a winery for a welcome drink. Kostas was always available and answered all of our questions quickly.
Word to the wise - we ended up renting a car to explore the island. We rented from Euro Dollar (big yellow sign very close to Kostas' place) - do not rent from them. They had terrible customer service and made us pay for a new tire when we got a flat even though we purchased the insurance. They also told us to wait on the side of the road for over an hour so they could bring us a new tire. When the guy finally showed up he put on the spare and told us we needed to take the car in to the shop the next morning. Giant waste of time overall.
The cave house is as depicted in the photos - our only problem was that the wifi didn't work on the second floor. Kostas said we needed to plug something in, but we didn't bother to try. So I'm sure that could be fixed. I would definitely recommend this place to any of my friends visiting Santorini.