Shivpuri Rishikesh but I'm not sure about it whether it's best or not becoz I never experience that, but if you want to camp in the woods then book a hostel or homestay at Manali, Shimla,jibhi which is hosted by a traveler itself believe me that will gonna be the best experience and also you can make friends.
Hey Nikhil, These are the places where you can enjoy camping near Delhi : 1)Prashar Lake-Hill Camping -HP 2)Rishikesh-River side camping-Uttrakhand 3)Mukteshwar-Hill camping-Uttrakhand 4)Jhajhar Khas-Desert camping -Rajasthan 5)Mussourie-Hill camping-Uttrakhand Hope this helps.