HI Ajay, you can head to Narkanda, Chitkul, Kalpa or Palampur, you can also witness plenty of snow in the first three places. From Palampur you can get incredible views of Himalayan peaks. The 5 day trip can be done eaily in 7-8 thousand rupees if you are travelling in public transport and staying/eating in decent hotels
Jibhi and Tirthan valley are good travel unexplored locations in Himachal Pradesh. You'll find peace there also there are good staying options with itinearies. Hospitality are very nice and locals interacts with you with joy & happiness. Suggesting you to find & search about these 2 locations.
I just did a Chopta, Tunganath, Deoria Tal trek in Uttrakhand. Bhowali, a village near Nainital is also a good option to travel to in Uttrakhand. Both of these options should be less crowded during the time.
Don't worry as December count as an offseason for north places so there is very least possibility that you get stuck on a traffic or can't find buses or cabs but if you really want to explore some peaceful and less explored places then definitely I'm gonna recommend you to go Jibhi or Tirthan Valley. This is gonna be your best experience if you ever been in Shimla and manali becoz Shimla and Manali is now a city full crowded but in tirthan valley, you will find some really surreal meadows. So go ahead.Happy Travelling!!
Best place and the most beautiful place is Spiti , HP .
Although it requires a week time minimum. rough budget would be 10k Prini , Grahan , Srahan , tirthan , jibhi , dalhousie , khajjiar ( hp) , sanjh , chitkul
munsiyari, chakrata , auli (uk)