Dehradun to rishikesh to auli to rudraprayag and yes Char dham are not to be missed and when it comes to Himachal: Don't miss manali , parvati valley , spiti valley, khajjiar and specially my favorite triund ... Its the list and you can choose the places which you can manage and you can miss , it all depends upon how much you wanna travel from one place to another and your budget.
Happy Traveling !
In HP you can cover 1. Chandigarh, Shimla, Kufri (3 days)
2. Manali, Kullu, Nagar, Manikaran, Solang valley or Rohtang Pass (Pass is opened depending on the weather) (3-4 days)
3. Mcleodganj, Triund trek and paragliding in Billing and Dharamshala (3 days) You can cover all the above and nearby places in 15 days considering the travel time and convinience.
Do visit Dharamkot, ahead of Mcleodganj. It is less crowded than other Hill stations. Though small in size but the town is serene. They have couple of cool cafe's too. Also plan a day for Indrunag. People visit dharamshala but never visit his place. U can actually see the whole Dharamshala from Indrunag .The road to this place has a steep gradient but it's worth a ride. One can also enjoy paragliding from that place.