I think if I were to have taken this trip again, I would have done it backwards, starting in Cordoba and ending in Granada. Granada and Sevilla had so many incredible things to offer that it started to make other beautiful things seem less impressive. It could also have had something to do with the fact that we were getting a little worn out from our vacation at this point.
Cordoba's main attraction is the "Mezquita" or the mosque. More specifically, it's a cathedral that was once the grandest mosque in Al-Andaluz. Unfortunately, as a cathedral, it just feels very awkward with the grand Moorish architecture mixed in with Catholic images. This place would have been very impressive to us if we hadn't seen any other Arabic architecture in Spain, but after wonders like the Alhambra and the Alcazar of Sevilla, this was a bit of a disappointment I hate to say.
Cordoba also had a bit of Jewish history to discover. We found the (very hard to find) synagogue that remained hidden for many years and was discovered in the 19th century. Remember that once the Catholics took over Spain, the Spanish Jews were forced to either get out, convert or face the consequences. Before that, though, there was a vibrant Jewish community of Sefardic Jews in Spain who even brought back the Hebrew language which had more or less died out by then. The House of Sefarad which is next to the synagogue gives a great history of Jews in Spain.
The famous image of Cordoba is of the Puente Romano (Roman Bridge) which connects the old city with the other side of the river. It's the view that always comes up on a google image search. While of course it's been updated since Roman times, it's still incredible to think that a bridge that old has still stuck around.
So, of course, Cordoba is a must see of Spain. Just don't do it after you've been to Granada and Sevilla. And especially don't do it when you're travel weary.