Hey. December is a good time to visit any of the north-eastern states. It'll be a peak season, with all the travelers exploring the best out of this side while experiencing the Christmas and new year celeb. Remember to plan your bookings in advance.
Well, Sikkim as a Whole is so tiny that you might consider it as a whole to do location in itself. However, Since it's peak winter time so maybe the High Altitude treks and Areas might be Inaccessible, in part due to the cold and in part due to snowfall. However, of recent, I have started recommending people to do more of the south and west Sikkim, primarily because of the low tourist crowds and also due to the beauty of the place too and ease of covering south and west Sikkim in One go. You, however, do not mention if you like long walks, adventure, and other things so it is pretty tough to recommend things. However, I would list down things below 1) Paragliding- Winters are really clear so this would be a must do, esp for the joy of flying. 2) Rafting- If you have a thirst for adventure 3) Walk to Bhaley Dhuunga-- its a one day walk along forest trails, so you do need to be reasonably fit, it is amazing if you enjoy forests and great views 4) Darap Village- Primarily because as an alternative to Pelling and also due to the nice village atmosphere and nice people 5) Kecholpheri/Yuksom/Tahiding- Nice locations and places to see 6) Rhabdentse/Peyangste- Nice places to see 7)Ravangla- Nice place, you would be staying here if you intend to walk to bhaleyshungaa, Also the Buddha park is here.
December will be the best time to visit Assam and Sikkim. but if you want to explore something different, then visit Meghalaya in Monsoon season. generally you can visit Meghalaya in December, but you will find some different things during monsoons..