Though I have not yet stayed there, (have made reservations for April), I recommend checking out Hostal El Reposo de Bagdad. Check out website at: "2abookings.com". May also be a link from this website, cant recall. We have a confirmed reservation for 35,99 euros/night for a double with bath en-suite. It is located at Fernandez Ruano 11, a fairly good location according to the map. Only 15 rooms, non-smoking room, Andalusian patio, all in all, sounds nice. Check it out. Good luck.
