I've stayed in Antalya about 5 times but never in wintertime so I cannot comment about the weather but there is plenty to see there, it's a real cultural trip.
The last time we stayed there we stayed with my Turk husbands friends a bit out of the town, loads of character but not much to do if you're on your own looking.
Have you had an xmas in Turkey away from the tourist areas? If not I'd urge you to really think about it, the only time we have was when we lived in Kizkalesi, impossible to find anything slightly seasonal (as you'd expect), no celebrations or atmosphere at all, unless you have a husband who's prepared to go chop a tree down on xmas eve and decorate with cotton wool as a surprise like I did

New year is big though so you can certainly celebrate that big stylee, lol!
Antalya is very expensive though, the dearest place I've been to in Turkey.