Bombay (now properly called Mumbai) is a city of great contrast. One minute you can be surrounded by poverty and the next minute you can be in a cozy restaurant enjoying great food and wine. About 60% of the population lives in the slums. Most other people live comfortably in large apartments, and they typically have drivers and servants (such as a cook). Meals are usually really cheap or fairly expensive. And most visitors of the city are said to either love or hate it.
Mumbai is also the glamour of Bollywood cinema so if possible it would be nice to try and experience Bollywood (and hopefully be extras in a Bollywood movie)…would be fun.
There are shopping malls full of designer labels, cricket on the Oval Maidan, promenading families eating bhelpuri or having the famous Bombay Burger or the traditional masala chai teas and the masala dosais on the beach at Chowpatty, red double-decker buses queuing in grinding traffic jams and the infamous cages of the red-light district…..
It's a city with vibrant streetlife, India's best nightlife, and a wealth of bazaars. Outdoor bazaars top the list of attractions for the bargains for example shopping in Fort/ Colaba neighborhoods… you'll find very inexpensive scarves, necklaces, t-shirts, leather sandals and anything touristy. You can do some bargaining [which is fun], but at a certain point it doesn't feel worth it to make a fuss over what's only worth $1 to a traveler, even though if they are technically trying to rip you off by their standards….so have fun and just give in gradually…..
More sightseeing options are the Gandhi Museum, in the leader's former home, and the cave temples of Elephanta Island. For tranquility, Mumbai has many religious sites, lakes and parks. Popular waterfront destinations are Marine Drive, where visitors go to watch the sun set over the Arabian Sea, and the carnival-like Juhu Beach.
And for those inclined towards the media. Mumbai also enjoys an array of media in print and on the radio. English speakers are spoiled for choice as the major national papers have Mumbai bureaux and there are various English-language local papers and magazines.
November through March is very good. It is peak season, so make sure all your bookings are done in advance. Prices are higher at this time, of course.