We will be driving through Cordoba on our way from Madrid to Seville, so we only have a couple of hours to explore the city. Some things on our list include the Alcazar, the Roman Bridge, the medieval Jewish Quarter, and the Mosque of the Caliphs. Are there any other must- see places you would recommend given the short time we will be there?
Given that you only have a couple hours, I think you've filled your list fairly full. There's a tiny little synagogue in the Jewish quarter that is one of only a couple remaining synagogue's in Spain that will take all of 5 minutes to see, but really, if you only have a couple hours, do what you can on that list, then find a nice tapas place and enjoy Córdoba.
You can spend a couple of hours in the Cathedral-Mosque of Córdoba - I did last summer - and given it's one of my favourite buildings in the world I wouldn't try to pack any more in. From the relative calm of the courtyard with its citrus trees, to the endless arches of the interior, the remarkable prayer niche and the absolutely hideous cathedral plonked right in the middle of it, it's more than enough to fill your time.
If you're driving there, you'll be able to find parking (free) on the other side of the river along the Avenida de Granada if you're happy to walk a bit.
Mentioned in this answer: