As much as I love Cadiz I'd take a day (or even 2) from Cadiz, add to Sevilla and visit Cordoba. Cadiz is wonderful but it doesn't have the number of sights (and incredible food) that Sevilla offers. I'm a slow traveler and Cadiz is probably my favorite city in Spain (Sevilla and San Sebastian also in close competition) but 4 days would be plenty for me. Sevilla also has many daytrip possibilities - for example I'd visit Carmona or Ecija over Medina Sidonia. Osuna is another place easily accessed by Sevilla and not often visited - I'd also prefer it over Medina Sidonia. And I'd put Cordoba in front of any of the daytrips you could do from Cadiz or Sevilla.

Just my opinion.

Thank you so much CathyM, you've been a wealth of knowledge on Andalusia!! I will take on board your comments and see what I come up with, the trip is not for another 4 months anyway so I've plenty of time to think about it!!

Thanks again.