Cordoba pays for a good walk around. It does not really go in for grand squares or grand buildings, other than the Mezquita and the Alcaza; the Alcaza was OK but I was not that gone on it.
The charm of the city lies in small squares and small churches, as well as the Judería and the bridge which I have already mentioned, and perhaps, above all, in the domestic patios.
It is possible to see most of what you want in a couple of hours; I recommend the old walls, the Judería, the tiny Street of Flowers (I have only seen it in winter but not a square inch of wall space appears to be wasted), as many patios as you decently can, the Plaza de Poltro (colt - after a sculpture - there is an old inn here mentioned in Don Quixote) and a few of the old churches, some of them converted from mosques.