We highly recommend Chrysoula’s apartment. Great location atop the Chora, and awesome hospitality. Chrysoula and her husband are some of the best hosts we have ever met and they are very welcoming. On multiple occasions they offered us great Greek food cooked by them, which was incredibly kind.
The house has a nice traditional taste and is always refreshed by wind.
The only tip, in case you decide to stay here: make sure you don’t mind walking steps as the house is in the middle of the ancient town and can only be reached on foot.