It totally depends on 2 factors: First your preference for the topography: Mountains: If you like Mountains then Winters is an epic time to cover the beauty of Sangla Valley, Spiti Valley and Ladakh. These three are once in a life time trip and in winters with snowfall it is just epic to be there. Beaches- 10 days in Goa, Kerala, Andamans and Lakshwadweep are just perfect for some fun time. The 4 destinations are meant for a perfect 10 days trip. Rajasthan- The trio of Udaipur, Jodhpur and Jaisalmer is normally considered at its best in winters during december. Rann of Kutch: The white salts will take your breath away. The trip can be combined with other places like Somnath and Dwarka :)
There are many places that you can visit if you want to spend time amidst nature. Kerala is a good option. You'll get a variety of options between hill stations and the beach. You'll find options for cave exploration, visit to national parks, stay in tea gardens, go for treks, or spend time on the beach. If you'd like to explore unseen places, then northeast is your best option. You'll find some of the most beautiful sceneries in places like (or nearby) Gangtok, Kalimpong, Kaziranga, Shillong, Tawang, Dirang, and Imphal. However, these are mostly hilly areas (except Kaziranga). The advantage you'll have in northeast is that in 10-12 days you'll be able to visit at least 3 or 4 places easily. You already have some good options in previous answers, so this should give you more options and hopefully help you plan your trip.
This is a 10 day trip. I am sure you'll love Himachal with its beautiful and serene snow capped mountains in the month of Dec. Do let us know if you plan it out.