Though it was closed indefinitely when we last visited, you may be able to climb the cathedral 's Torre de Poniente for fabulous views over the old city with its many 18th-century watchtowers (built so citizens could keep an eye on shipping movements without stepping outside their front doors). Back then Cádiz had 160 of these watchtowers: 127 still stand.
It's next to the main cathedral entrance on Plaza de la Catedral.