We stayed for a week at Kristinas Room with Anastasios, definitely a must stay in Rhodes.
It is in a perfect location, walking distance to everywhere in the old town and new, but far enough from the busier streets to allow for a quiet retreat for food or a nap. All meals are offered and for a very fair price, and if mentioned to the hosts beforehand, they can have breakfast ready and waiting for you in the morning.
The rooms are cleaned daily, so you always come back to fresh towels and a made bed.
And best of all, Anastasios offers an airport pickup service that takes you right to the door of the hotel, an impressive feat considering the tight streets of the old medieval town.