Rajasthan,goa,gujrat,kerala,northeast,himachal,andamans december is good month to travel pretty much most of the places other then high altitude even those places are good if you enjoy chill weather
Auli in Uttarakhand (i recently travelled there in january... you can check out the trip on my profile) Also other places in uttarakhand like Chopta, Kausani. Shimla-Manali In Himachal Pradesh. Spiti Valley if you are an experienced traveller and ready for worst cold temperatures.
If you are looking for an offbeat place, try out Auli. Light snowfall during December makes it look like a white heaven. You can even enjoy camping and skiing here.