The place is cozy and nice - we loved everything and the only negative things I may say are trivial (they are just a "heads up" to future stayers rather than negative remarks). First of all, the host was very accommodating and friendly. Our flight was coming late at night and the ability to check in late is a big plus.
Everything is modern and clean. When you walk in, the first room doubles as a living area and kitchen and also has a pull-out couch, the second area that has a bed is divided by a wall and some windows but it is fully open, so do not expect complete privacy if staying with multiple people/members of family.
Keep in mind, it literally is a cave in the sense that it is built on the side of a hill/mountain, so the only windows/doors to the outside are toward the front, where the front door and bathroom is - this leads to a bit of a claustrophobic feeling but you get used to it quickly. There is a DEhumidifier in that second room - it is very humid on the island and even more so in the cave - that water tank fills up in less than 24 hours, make sure to dump out the water or else it will feel too humid (there is an indicator at the top that lets you know when it is full).
In the bathroom, if you, like me, are not careful/clean when you wash at the sink and let water spray around, keep in mind that the toilet paper is right to the left and below the sink shelf, so it will drip on the toilet paper - put a rag or a paper towel there to soak up the water before it drips on the toilet paper. If you are careful while washing, you don't need to worry about this.
The road to get to the house is VERY narrow between hills/mountains and has twisty turns with lots of blind corners that only one vehicle will fit through. As a European, people may be used to this, but as an American, it was terrifying to navigate in a rental car, particularly because the locals/other tourists drive way too fast around these blind corners, so just be careful, drive slow, and get ready to hit the brakes if someone comes flying around that corner. Chances are, one of you will need to back up to a wider area of the road to let the other one through. This is where smaller vehicles shine - Santorini looks like it was made to be driven on ATVs - lots of steep hills where 4x4 is a Godsend and lots of narrow roads that are not a problem for ATV width but hard for full-sized cars to navigate. We found a neat spot on the street to park just 10 meters from the house, though that spot is not always open, so you may need to search for a place to park if you came in a car.
Lastly, I wanted to mention that you are not far from a church at this location (this will be true just about everywhere on the island - the island is not big and yet has over 300 churches on it!) - the reason I mention this is because the church was ringing bells for what felt like a full hour in the morning followed by some chanting - if you ask me, you should be up by that time anyway, you're on Santorini, don't waste your time sleeping, there's lots to see! But you should know that you may be woken up by church bells around 8 or 9. This did not happen on the second day.
Overall, the place was amazing, it's near the airport and somewhat at the center of the island, so if you want to see more of the island, this place is perfect because it's a fairly short drive to everywhere! The place inside is well-made, modern, and pleasant. It had all the normal amenities you would want while traveling, including WiFi and a washing machine. Would definitely rent again if I ever come back to Santorini - highly recommend!