Hey Niyati, There are many to see in Himachal Pradesh as off beat destinations:- You can take this spiti circuit easily through public transportation only:- Start from Shimla ... then reach Jeori or Narkanda and then go to Sangla ... and then to Chitkul ....Stay in Chitkul for a day and enjoy the last Village of India .... From Chitkul you can go to Tabo or Nako monastery depending on the buses available for you ...Stay a day der .... From Tabo u can go to Mud Village and have two days there and also enjoy the national park visit ... From that Village go to Kaza ... Get a car for a day there and visit Kee monastery ... Komic Village for highest post office ... It will take 2 while days to enjoy Kaza ... And then your stop can be to manali directly or if you have time visit Chandertal lake and stay there a night to view the splendid Milky way of stars ... From there reach Manali via Rochtang pass .... So this is a chunki of less visited places in Himachal Pradesh which would be an adventurous one also in one's life time .... Apart from spiti valley you can visit Khajjiar ... Bir billing Dharamshala Mcleodganj Kasol Kasauli Beas kund valley Thirthan valley and many more ... As your question is for December, please check the road status before you plan and leave .. Tripoto forum is also der to help you again ... Happy Travelling!!!
Best is start from Chd then go to AUT(From here enter the Trithan Valley),from here go to Mandi(From took a bus to Baggu then to PrasharLake trek),go to Bhuntar from here(Entry to Parvati Valley),Then go to Manali.After Manali You can go to Spiti valley,Macleodganj,Shimla depending on how much days u have.In each valley there are many hill stations,You can give atleast 3 days in each.Acc to me Best is go to Trithan valley and Parvati valley.