There is a lot options, but could b better if you let me know what do you want to do in Cordoba.
Anyway, I recommend Mediterranea Cordoba Hostel: Its a small hostel and also it has private rooms. (it has pool too, but it's cold at this moment). Check www.mediterraneahostel.travel to know more about this place. It's small, and the managers are a family.
Other option is Link Cordoba Hostel. It has a pension area, and the common facilities that any hostel has.
Hope i can help you. Let me know if you need something else. May be you are looking for some special lodge. Let me know your needs. about 8 years ago