The Cloister Inn hotel was exactly what I wanted, and even exceeded my expectations. It is located right in the middle of the old town, and it has two rare features in this price segment: private parking and safe in the room. Just do not forget to call the hotel in advance and to reserve a parking spot. They have just 8, or 10 of them.
All scary tales from other reviews did not materialize in our case. The room was clean and spacious. The ceilings in the rooms are at least 4 meters high. Looking out of the window I saw the quiet backyard with our car parked in it. I did not hear any noises from the street, or from other rooms. The air conditioner worked just fine. The breakfast was very good. The safe and refrigerator also worked as expected. My extra thanks to Ahmat at the reception desk. He was very polite and helpful.