Hi and welcome to the forum!
My first recommendation is the car hire Malaga
option. Yesterday I visited as example Montilla in Cordoba
and It took a little more than 1 hour to get to Montilla from Malaga. I like visiting small towns also, so a car rental is a must if you really want to visit white villages without spending much money.
My recommendations based in my experience are:
In summer Tarifa, the town is very nice and there is a surfer ambient everywhere.
Nerja worth the visit in summer or winter.
Sierra Nevada in Granada is a must in winter.
If you like small villages really, Otivar is a very nice and very recommended visit, I loved the trip and I got there driving from Granada
by a mountain pass to Almuñecar.
Nightlife in Malaga:
There are comedy clubs in Malaga
, I can recommend one if interested.
About the live jazz and live music or festivals, I recommend to check our blog as I use to post those events there. It is updated every day or every few days: http://www.malagaweb.com/blog/tourism/events/
There are many cinemas in Malaga, the cinema where I use to see the films is "Plaza Mayor", located between Malaga and Torremolinos, you can choose to see spanish or english films, and we have 3D or HD as options for watching the films.
Finally, if you are not after the beach and the sun, just for visiting small villages and experiencing Malaga itself. February, March or April
are excellent months, January maybe its a little cold and rainy here; September and October are nice months too. All those months are not too hot neither cold.
Hope this information helps.
Let me know if have more questions, and remember to make your hotel and car hire reservation ahead of time.