We had a wonderful time at Andromahi's cave home - it was clean, adequately spacious for the two of us, and well-equipped; Andromahi even bought an espresso machine after we asked if she had one! When my bag didn't arrive when I did, she and her assistant, Anthony, found a service nearby that would pick up my bag the next morning for less than half the price of me going back to the airport to retrieve it.
Anthony also assisted us in booking a side trip to see the island.
The cave is perfectly located: close to all the interesting shops and restaurants of Oia, yet very few people passed by us because there wasn't much below us.
The balcony views were stunning; the only drawback is that Andromahi's other cave shares the balcony, and voices of the neighbours carry over to our cave. Other than the sound issue, we had a fabulous stay, and were made to feel very welcome (beginning with the wine and fruit left for us at our arrival).
We would definitely recommend this accommodation for anyone.