You've got mountains "nearby" in American distance (i.e. few hours drive) almost anywhere in Spain.

Madrid is less than an hour away from the Sistema Central, a mountain range crossing northeast to southwest around central Spain, dividing the Central Mesa in the Submeseta Norte and Submeseta Sur. It's not the tallest mountains of the country, but they're still quite respectable with the highest peak, Peñalara, rising to 2400m above sea level.

I can't guarantee sun in winter anywhere in Spain, that depends a lot on how lucky you get, it's like a 50/50 in most regions outside the north which is cloudier.

Regardless of your choice of stay: welcome whenever you arrive!