Mumbai is a city of some 18 million people, and almost the same number of attractions to explore, ranging from museums and parks to the crumbling bazaars and natural features.
Chowpatty beach is one of the least pleasant places in the city during the day, but at night it fills with locals and stalls selling everything from food to massages, and is a great place to hang out and people watch.
Just outside the Taj Mahal Hotel on the Apollo Bunder seafront, you can see the famous Gateway to India monument built in 1911 to commemorate the visit of King George V. It's a unique archway that owes more to Gujarat architecture than to British influence, and is a place that is thronged by hawkers all day long, but is an essential photo spot for all visitors.
Another great sight is the shrine of Haji Ali Mosque, which rises out of the sea like a marble ship, and is connected to the city by way of a causeway only navigable through a swarm of beggars at low tide, but well worth the trip.