Agree re la carboneria - great place. Conil is great too but quite some drive away. I did it on a separate trip.
Having been to seville, cadiz, jerez, cordoba and granada (twice), I would chose cordoba and granada every time but seville is still great.
I would very much disagree with Clapham's point 5. It's surprisingly big. Imagine the lanes but a thousand times as big. Expect to get lost but enjoy it.try a dozen tapas bars a night. My favourite was el riconcillo which was also on rick stein's spain.