Ioanna and her Husband Fotinos' cave house was a nice stay. It was a bit more expensive than we wanted, but you definitely pay for the location and the view. The view was top notch, amazing private view while sitting on the rooftop. There is even a small terrace which you can put a small table and chairs for evening drinks after the sun goes down.
The cave house was clean and tidy. A little bit outdated and the Wi-Fi was not good - I believe the router was in their office which is just outside the front door of the house, but the rock walls do not allow for signal to pass through well. If you are tall, be prepared to duck often. I am only 176cm tall and I hit my head on the doorways more than once... and unfortunately ruined a pair of sunglasses.
However, it provided all the things you needed and was quite comfortable. Again, location is key. A short walk to the parking area, various restaurants and shops, and they Byzantine ruins are right next to the house (Amazing sunrise view from there).
Ioanna and Fotinos were very nice. They even helped us book a fishing tour, which we were able to catch some fish on a private boat, do some swimming, and even watch the sunset from the boat. Amazing trip!