Hi Ajay, If you're planning to explore North India in Dec & Jan, you'll surely be greeted with the chills. Most of the hill stations in Himachal and Uttarakhand would be super cold, and some would even be covered in snow. However, Manali, Shimla, Mashobra, Mcleodganj, Kasol, Dalhousie, Mussorie would be good to visit.
Otherwise, you can head to the beaches. Goa, Kerala or Pondicherry would also be great :)
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U can visit Udaipur city of Rajasthan , it's looks beautiful at a time of winter and there are many places to visit and shop around the city . and it's winter is to remember .... because it's full of lakes ..