Aside from the Mezquita, Cordoba has a few other interesting places to check out. The other thing I checked out is the Alcázar de los Reyes Cristianos, which is a medieval palace ("Alcázar" after all comes from al-Qasr, which means "the Palace"). This building is a fortress, which served as the primary residence of Isabella I of Castille and Ferdinand II of Aragon.
This fortress was constructed in 1328, by King Alfonso XI of Castille. There used to be an old Visigoth fortress in the location. And during Isabella and Ferdinand's times, they used it as their headquarters against the Nasrids.
The gardens are quite cool, with elegant fountains and ponds. The garden used to be an orchard, but now it's a great place to meander and explore. There's numerous cylindrical cypress trees that form the so-called King's Walk.