When considering the Costa del Sol out of season, ie November to March, best to base yourself in the busier 'working' towns like Fuengirola and its environs, than, say, Benalmadena where the visitor numbers and a lot of bar/restaurant opening hours rise and fall with the mercury.
A good compromise would be Los Boliches, one stop and two mins on the train from Fuengi, or a 15 min walk.
LB is lovely in winter with its atmospheric little bars and restaurants. You can walk the beach/paseo to your heart's content or for a longer stretch, take the train to Torremolinos, walk along the promenade, thru the marina, to Benalmadena, then uphill to Arroyo station, stopping for drinks in Bonanza Square (Legends or The Feathers) or further up at Avenida Gamonal for delicious tapas in The Wine Bar, then train back to LB.
A good two and half to three hours... or do it in the opposite direction... if you are feeling especially energetic, push on from Benalmadena along the coast road back to LB (averting your gaze, or otherwise, at the Nudist Beach, conveniently signposted)
Close your eyes and take your pick of the little backstreet bars in LB, a personal favourite, due to the sporting theme, being Alley Katz. Some smashing, good value restaurants, too.. just check the menus and prices and take your pick.
Accomodation-wise, look first at the Nuriasol, reviewed here and on TripAdvisor