IIT Bombay is located in Powai Area and as you know Powai area is one of the top areas in Mumbai.

There is Powai lake where you can hangout or even relax in evenings. Actually it can be seen from the Hostel's itself.

Then there is Hiranandani's Garden where you can find each and every you want. There's restaurant, Cinema Halls, Mall's, Top notch showroom and what not.

So, just enjoy.