I'll throw in probably my favorite, or at least top 3, cities in Spain: Cadiz.
With 9 days you should have plenty of time for several daytrips. But the great thing is that you really don't have to plan them in advance and can wing it. The exception being Cordoba where you'd want to purchase train tickets in advance.
I'd also agree with the suggestions of Jerez, Arcos, Sanlucar, El Puerto, Ronda. The sherry triangle towns, my favorite being Sanlucar, would be a great insight into the sherry culture. And Jerez is strongly influenced by the spanish guitar.
The high speed train to Malaga is about the same time it takes for bus or train to Cadiz. But there's alot to see in Malaga and personally I prefer laid back Cadiz with it's slightly crumbly but characteristic old town.
A couple of other places more off the beaten path: Ecija and Osuna.
All of these places can be done using public transportation if you don't have a car.