What's your target price range? Under 20 Euros per night? If so, you're definitely considering youth hostels. If you can spend a little more (and want that private room) you'll be considering hostels (called "hostales" in Spain/Spanish) and pensions ("pensiones"). Seems to me a few of them have been reviewed here in the past. Try a SEARCH using keywords HOSTAL CORDOBA and you should find them. Also, check the list of those which have websites @ http://www.SpainHostels.com/links/Andalucia/Cordoba/Cordoba/

Good luck! Saludos, MadridMan