We had a great time staying in the White Cave, and the name is spot on!
The apartment is the size of a small studio and has everything you would need, even including a washing machine and ironing board, cleverly integrated into the space. The bed is also huge and very comfortable.
The location is perfect for exploring the Old Town, close to the windmills and lots of really great seafood restaurants.
Check in and check out was super simply, Andreas and Valentina were very welcoming, made the the process super simple and were always fast to respond.
Overall I highly recommend staying here if you want a great value for money while exploring this part of Mykonos!