There are quite a few places u cud visit
Gateway of India
Quite a few pubs in that area like Leopold, Mondegars. These pubs are open from around 11am and you will enjoy the retro styling of this pub.
It has been raining there quite heavily these days. I always have hated the rains :). There is a famous hill station called lonavala, around 3hrs drive from Mumbai.it's best visited during the rains. There are quite a few hotels in lonavala as well but they are booked especially during weekends. Quite a few nightspots in Bombay Overall ur hotel will be able to provide u all the info u need :). There is also a museum in the town area of marine lines/church gate. also you Can visit the suburban area of Bandra, where there are a lot of pubs.
Remember...Bombay is a dirty and crowded city but the people ther are very helpful and overall a very safe place to wander. It is a city with tremendous energy and is Extremely fast paced. It is a city that grows on you:)
Do try the local trains to get the feel of the crowd. Not recommended if you have a weak heart:)
All the best and do let me know how adventurous your trip was
cheers about 7 years ago