Boulder Box, located in Vasant Kunj, is the kind of space you'd go to if your idea of fitness goes further than just the gym. They've got an exercise room for strength training, yoga, and endurance training (they have a trainer and conduct classes for the same), a cafe that serves coffee and light bites, and even a small library on the second floor.
For the main part, they've got bouldering walls spread over two floors—you can actually climb the wall from one floor to another! They've also got something called a Moon Board, which has lights on it to guide your climbing route—a fun challenge. They conduct classes, provide all climbing gear, and have changing rooms/showers, too.
They're also got aerial silk, but we say leave that to the pros, unless, well, you are one.
Their membership charges are INR 500 for a one day pass, INR 4000 for one month, and they've even got 10-punch pass that's got an infinite validity.