As you all know, you are coming to the most happening cities in India. And you might want to explore it all before you leave, unlike most who keep most of it hanging till their last semester here.
There is lots to explore, a few genres indicated below:
1. Beaches (personally, I prefer the ones just outside Mumbai)
2. Malls for shopping (girls, yes girls)
3. Food (every damn cuisine)
4. Hills to trek
5. Party destinations (down south Bombay)
These are just a few, specific details can be discussed on demand.