Answers:

Oh Wow, Cadiz is a beautiful place, the old town is in the tip of the peninsula, there are many plazas that are always full of life. To get to the old town you must pass through the new town, it has excellent beaches, although a bit chilly in January!

It is a shame you will miss the carnival in February!

Five things to do:
  1. See the Cathedral, a sandy-yellow church that is much bigger up close than you would at first think.
  1. Climb the Torre Tavira, the highest of the old watchtowers, with a panoramic camera showing 360ยบ live pictures of the city.
  1. Go to the beach. Stick around until sunset, which should be enjoyed at Caleta beach.
  1. Take a virtual tour of 18th century Cadiz with a 3D video of Cadiz at the city walls.
  1. Eat the fried fish, in particular at the Freiduria Las Flores on Plaza de Topete.

From there you could go to Tarifa, Algeciras for connections to Ronda, Gibraltar, the costas and from there you could also go to Seville.

If you do come down to the costas we have a 3 bedroom townhouse there available for rent :)

Have a great time you will love Cadiz, it is a wonderful place.

http://www.3bedroomtownhouse.com

Take care and have fun!

Simone Icough has gotten 1 cheer on this answer.