I think best place is Cannaught Place, where you can rent on a bicycle or scooty and roam around freely for hours. It has variety of cafes - my personal favourite is Cafe Hawkers. Moreover, a lot of stalls for street shopping. It's a perfect place to enjoy!
1. You can go clubbing to Toy Room, BW, Kitty Su and more.
2. Enjoy dinners in Mehruali at We Qutub, Dramz, etc.
3. Have a day time picnic at Sunder Nursery and Deer Park.
4. Can enjoy YULU rides in CP and near India Gate.