For starters, if you can, get yourself a Lonely Planet Mumbai.

Few of my suggestions though:

1) A nice boat ride from the Gateway of India. This also goes to the Elephanta caves, but I've heard the caves themselves are a bit of a tourist trap (never been there myself)...

2) Dinner at the Peshawri (Grand Maratha Sheraton by the Intl Airport)

3) Catch a bollywood flick at one of the Art Deco cinemas, even though it won't be subtitled. I think the refurbed Metro should be a good option

4) Wander around the museum area (Kala Ghoda, Asiatic Library, Prince of Wales museum, art galleries, etc)

All the above except 2) are close to where you'll be staying...