If you are coming to Mumbai then
1. There is plenty of hiking/trekking to be done during cold days and monsoons in Sahyadris. They offer stunning views.
2. Go to local clubs/pubs
3. Barbecue party on terrace (My favorite during winters)
4. Watch a cinema every weekend.
5. Invite friends over for movie marathon
6. Get a job. (It's fun to earn some money)
Mumbai is supposed to be really beautiful, unfortunately I'm going to Chennai.
But I plan to visit Mumbai at some point during my stay, since my friend has a house in Mumbai. Barbecue sounds awesome, I love food. 😉