Hi Jeff......
If you aren't worried about nightlife, etc..... i would recommend spending time an hour or so drive further inland.
Ronda, Grazalema, Zahara, El Burgo, Olvera are all towns set in a beautiful mountainous area. The roads are for the most part in great condition, and traffic is almost non existent. They call the area the lake district of Spain.
I am biased though, as i have a base in Olvera, and bought here specifically for the great cycling/motorcycling roads.
The other great thing about this area is that you are within 1 to 1-1/2hrs of Sevilla, Malaga, Cadiz, Jerez, Granada, Huelva, Cordoba and all of the coastal towns such as Marbella, Estepona etc.
I believe the Granada area is also very good for cycling, but i havent explored that area yet.
Oh one other thing......it can get pretty cold here in the winter. I set off New Year eve with a long sleeve cycling top and shorts and it hit -4 at one point (1150m).
Luckily i had taken arm and leg warmers.
Good luck with your planning
Dave
Ps....Sorry i cant help with any info on clubs etc, but almost every town and village have them.......