All depends on what you like... a trip to the Alhambra Palace in Granada is a good way to spend a day, but go to their website and book over the net 'cos the queues are horrendous if you don't. Alhama de Granada is a beautiful place with mud baths and beautiful lakes. Frigliana is a white village (a bit touristy but worth seeing) the list is endless! Best bet is to go to www.andalucia.com for places to visit. (We live about 60 miles away and have only done a fraction of the touristy bit and we have been here over 2 years) :o)
The caves in Nerja are a good way of killing half a day.
Almunjecar is good on market day
Also, we drove to Nerja from Granada thro the mountains and it was the most spetacular experience. Avoid the new motorway and take this road, you won't be disappointed.