I stayed in Hotel Maimonides
for one night last month. I found it on Expedia for a very reasonable price (about 62 Euro at that time). The hotel is right across from the Mezquita. It is nice establishment. The room was big and excellent. They have a restaurant on the premises and a nice courtyard. They also provide the usual amenties (safe, tv, extra blankets and pillows if necessary). The staff was very courteous and professional. It was by far the best place we stayed in during our two weeks in Spain and Portugal. Highly recommended for the price.