We had a lovely stay at Katerina's cave house. The best thing about this place its location in the traditional village of Vothonas. You feel far away from the loud, touristic scene of Santorini but physically it's quite easy to get to Fira or Kamari. The bus is a 10 minute walk through the gorgeous cobbled Vothonas streets.
The house itself was clean and comfortable. There is a nice shared courtyard which we would have loved to use, but unfortunately the amount of mosquitoes made this unpleasant.
Katerina was extremely kind and helpful with everything. She even drove us to the port when we left. We were so grateful.
Stay here if you want a more traditional experience on Santorini, but not if you want ocean views or to stay amongst the party scene.
Ps. Getting there from the port:
Katerina suggested we catch a taxi, however we didn't see any when we arrived. If you do not have your own transport, get on a local bus (dark green with yellow sign) to Fira, and then another bus to Kamari and get off at Messaria. Then walk to the house. This may be too much on arrival so you could also get a private car to drive you, which can be arranged at the tourist info places, but this is comparatively expensive.