We visited Kea and the mill for our honeymoon, and both agree it would be impossible to find anything more romantic and beautiful within our price range. The mill is situated very privately in beautiful nature, with a breathtaking view. Kea is a wonderful, peaceful place to be. Not many tourists, and people are friendly. Lots of things to do, like hiking, diving, boating, eating, etc. As others have posted, we recommend renting a car, as the island is fairly large, and the mill is a couple of kms from supermarkets and restaurants.
The best restaurant we found on the island was Kalofagadon in Loulida central square, the staff is nice and friendly, and the food to die for.
All the best recommendations from us. We hope to get back before long!