I agree with you totally, just last year I had gone on a three month hiatus to spain and in addition to learning spanish cooking, managed to see quite a bit of spain. Spanish history has always fascinated me and I have to say that to see the actual palace and the moor's last sigh was just fantastic.
Cadiz is indeed a beautiful place to visit and the cuisine there is great, the tapas at the various bars may take some getting used to in the beginning, but after that you will want to eat nothing other than tapas.
