Just explore the market and food there. Joshi's Momos are the one. Also you can have pineapple juice near Rajpur Road. And if you want to explore musoorie it is 2hr beautiful ride from dehradun. you can visit Lal Tibba, Gun hill point, George's Everest.
Honestly speaking D'dun is not that great to spend more than a day, i been to Uttarakhand in last week itself and ended not staying in D'dun, you can stay at Rishikesh as the vibes are so good and positive. In D'dun you can cover up robber's cave, sahastradhara, Tapakeshwar temple, Tibetan temple, Deer park, FRI. Rent a bike and roam all around. Also don't forget to visit Ellora's melting point.
Hi Ranjana, You will like the city for sure. However, I would suggest to book a hotel on Rajpur road. That is like the happening road there. You must visit the tourist attractions like Lachhi Wala, Robbers Cave etc. Also there are places like Shiv Mandir on way to Missouri, Sai Baba Temple, Tapkeshwar where you can go. To get a feel of Dehradun - do visit Kumar Sweets on Rajpur road and have the kulfi there. Visit Paltan Bazaar. Go to FRI, also pass through IMA. Eat the Bun tikki there and the fish fries from road side stalls. Usually there is some or the other trade fair in the Gandhi Maidan. Just check if thats on, and do visit it. You will have a wonderful time shopping. :)