Excellent adivce was already given by @Edinburger. It is indeed very easy to walk around Cadiz and the ship docks right by the historic centre.
Just regarding "What are the must sees?" I would add
the cathedrale museum
the tavira tower, equiped with a camera obscura
the Oratorio de la Santa Cueva, two hidden beautiful chaples on top of each other
Iglesia de Santa Cruz, the oldest church in Cadiz
Not a must see but a hint in case you feel stressed out by the Summer heat: right next to the historic city centre a huge beach area starts with restaurants, bars and so on close by,