When it was just me and the wife, we always hired a mini, its the perfect car for the Spanish medieval streets

Thanks for the advice, Puma. I looked at a map of the city and can see 5 or 6 parking garages noted. I am thinking about staying in the old section and parking outside the area in one of those garages - but also taking day trips with the car as well.

Day trip question: I plan to go to on the road from Cadiz to some of the nearby towns for a few hours each day. Is Jerez a day-trip type of town or is it worth a complete day and overnight stay? Any experiences or opinions?

... keep writing "Puma" .. mean "Puna" ... sorry!

it depends how use you are of driving in cities, to me its the best travel. I always use parking garages underground. you should know Cadiz is tight so spaces are limited, my best have been a while back by the plaza de la Hispanidad area. You can always contact the tourist office and ask them where is best to park a car today.
http://www.cadiz.es/Category/turismo/oficinas-de-turismo/547
hope it helps

Quevedo .. I would suggest that Jerez de la frontera is an easy day trip as it´s only 37km from Cádiz . But I have read that Jerez is a nightmare to park in and that you should definitely use the underground parking for which you´ll have to pay . Apparently the police in Jerez are very happy to tow cars away that are parked illegaly , so be careful !
Also if you don´t mind a longer drive you could go over the border into Portugal . Very near the border is a beautiful medium sized town called Tavira . Very Portuguese ! My cousin lives there and i´m planning on going there for summer .( I´ve been 3 times already )
If you decided on going to Tavira then that would be a full day and you´d probably have to stay overnight .

Thanks, Steve! I am going to be very careful about parking. I have been in too many tight spots in Spanish cities to take risks. Underground parking is the way to go. Let me look at Tavira on the map - thanks for the idea!

Quevedo,
if you've never been to Seville or Córdoba, I'd definitely suggest those cities, simply wonderful, perfect to relax and enjoy all senses.

Thanks! I have been to both and love them. I plan to spend a couple of days in Sevilla before heading to Cadiz this time. I appreciate your suggestion!!

By the way , the iconic Spanish singer Rocío Jurado who was married to a famous bullfighter ( Ortega Cano ) and died of cancer some years ago will have a museum opened in Cádiz in March of this year . I´m not sure exactly when . Rocío Jurado did a concert , her last, when she was diagnosed with cancer and was joined by very famous Spanish and Latino singers . You can buy it on DVD . She´s very Spanish , vey dramatic and it was an emotional concert . The museum is called , simply , El Museo Rocío Jurado .

but of course Rocio Jurado is a grand dame of Spain. She is from Chipiona near Cadiz, so with a museum going to Cadiz will be a lot more worth it.