If you don't mind a rain shower or two then January offers the chance to explore Atalaya without the big crowds getting in the way. An average rainfall of 240mm means you’ll probably need your brolly and it won't be freezing but might be a little cold.
Suggested activity: Stay indoors this month with a visit to the world class aquarium near Konyaaltı Beach. There’s a 130m+ glass tunnel you can walk through to get close to the exotic fish, as well as lots of other great attractions including a 3D cinema and an ice museum with its very own snowfall every night. Throw in snakes, lizards and crocodiles and you have a brilliant family day out.