The Hector Cave House exceeded our expectations and was the ideal place on Santorini for many reasons. The personal attention and responsiveness from Gianni, Dana and Dimitri was extremely helpful and warm, and unintrusive. The interior had so much character, and the condition (including the cleanliness, bathrooms and beds) was extremely comfortable and on par with what I'm used to in hotels. And the best reason to stay at the Hector Cave House - the terrace! I spent so much time alternating between reading in the plunge pool, napping on the bench under the umbrella and watching the caldera at all hours, morning and night.
Some tips: We went in early May, and it was comfortably warm. I think the summer is very hot so be prepared. May was also pretty crowded in Oia. There's not much to do about that, but being aware ahead of time might help with your enjoyment. I highly recommend taking Gianna up on his offer to assist with planning activities. He's very responsive and eager to help, and it was like having a local concierge, which made the whole time much more relaxing.
Most important tip: book early!