Any place in Western Ghats would awesome in winters. The temperature in hill stations and early morning sunrise in the Fog will make go crazy.. places like Munnar, Waynad, kochi, Coorg, chikmaguluru...
There could be no other place better than Kashmir(Just kashmir if less than a week, otherwise add Jammu as well).
You can start your trip from Srinagar. Flights to Srinagar are cheapest. Spend a day there, move on to sonmarg, gulmarg and pahalgam. If you will be lucky, you might experience snow fall as well. Security wise, only Srinagar is the place where I would suggest to be cautious, rest all are travel friendly. If not kashmir, go to Shimla, Manali and Dalhousie.
Western Ghats are awesome. Places like Kudremukh, Coorg, Chikmangaluru, Yercaud, Ooty, Kodaikanal etc are fabulous check out blogs in my Tripoto profile for more info