My wife and I went to Santorini for part of our honeymoon and Fanari was one of two places we stayed (the other was Canaves), because we wanted to experience them both. Each was a wonderful place, with Fanari being smaller, more intimate and more classically designed.
I honestly don't think anything about this hotel could possibly be improved! The staff was so nice and helped advise us on places to go, and when we arrived a bit late the first night, they still ensured we had some dinner. The food was excellent, they had the room STOCKED with complimentary drinks when we arrived, and one morning they brought us breakfast to our balcony...and I mean they brought us a little of everything they offer at breakfast to be sure we had what we wanted! Their service is almost ridiculous it is so good, but in a laid back non-pretentious way.
The facilities are impeccable and show a lot of character! The room we stayed in had a HUGE bathroom (both shower and tub), a sitting room area, a TV and DVD player, an in-room hot tub that was more like a pool in size (although they don't keep it steamy hot like they do in the US), a semi private balcony and THE sunset view of Santorini above all others. I say THE sunset view, because people will specifically come to this hotel to order a drink and watch the sunset, because it is perfectly positioned.
I had always wanted to stay at one of these world-famous cave hotels and this was such a dream come true, particularly being able to share it with my new bride. What a treat! I will definitely look forward to going back for our five year anniversary. I love Greece as whole, and I love Santorini (Thera) in particular.
(we actually went in October 2010, but the date selector does not seem to go back that far)