Cadiz is a great place to wander around and do nothing for a few days.

Like the first respondent says, Cadiz old town is beautiful, though perhaps a little chilly in January—but nicer than, say, Chicago at the same time.

1. The cathedral is fun.
2. There’s a ruin of a Roman theater behind it, or nearly so.
3. I enjoyed the Museo de Cadiz: http://www.juntadeandalucia.es/cultura/museos/MCA/?lng=es
4. Wander around the waterfront. I remember seeing parrots in a public park (Parque Genoves).
5. Wander around the streets. You can’t get lost since it’s on a peninsula. There are some really wonderful tapas places tucked away in the old town.

If you can manage Spanish, try www.infocadiz.com