If you want to stay in an Oia cave with a view I recommend Theodora suites.
Service is great and they go out of their way to look after you around the chaos of peak season. Very smooth operation and great room.
Only negative for the price we paid could have done with a little more privacy (we had lots of “visitors” getting their photos outside our room).
Again team are wonderful, are available to help 24/7 , leave no stone un turned, and navigate you towards best places . Niki in particular was a star! She even helped us to find a place to chill with a pool post checkout which was perfect.