We really enjoyed our time at Stathis place. The cave houses are very unique and the property is well kept and the small kitchen areas were stocked adequately for simpler meals. There are some cave house only kind if things we didn’t anticipate like open showers that you can’t fully stand up in and the inability to flush toilet paper down the drains, but i suspect that is pretty common for most of Santorini based on what we saw at other places.
My only complaint with this rental were the services we utilized based on the owners recommendations like the the transfer from the port, car rental were more expensive than my friend who stayed in the middle of Oia. Cost comparison his car 50 euro for 4 days, mine 30 euro a day, transfer from the port his 40 euro round trip, mine 90 euros round trip (which, Stathis covered 20 of) due to a mix up at the pick up upon arrival.
All in all it was a good stay and the place is sufficient to accommodate groups of people and good for families with kids.

If you interested in hiking the trial between Thera to Oia passes just up the hill from the road above the house and walking into Oia from the house takes about 12 minutes.