We recently had a five night stay at Anemomilos Villa and enjoyed every moment of it. It was a fantastic place to explore Santorini from and we could not have asked for much more.
We flew in late at night, but Petros from the hotel pick this up for a reasonable transfer fee of €15. The room was quite nice - seemingly renovated very recently and (while not of the sea) had good views of the surrounding area. The balcony was large and quite comfortable to sit out on. While the pool is on the small side, it has a good number of sunbeds and is good to cool off and on a hot day. Each room has its own wifi connection which worked very well for us.
The hotel is located in a very convenient area. It is in Firostefani, which is only a 7-10 minute walk to the main drag of Fira itself. It is very close to the bus route, and is also in a perfect place to do the hike from Fira to Oia. There are a lot of conveniences nearby, including little markets, car rentals and restaurants, not to mention a short walk to famous St Girasmos church (the blue dome one you see in all the photos of Santorini), as well as the shops and restaurants on the main walk along the top of the cliff overlooking the caldera.
Anna, the owner, was very accommodating and nice. Her English was very good and she was able to help us with anything else we needed. We thank her and Petros and hope to stay again soon.