I have visited the city three times and on one occasion I had to stay back for 10 months. There are lot of things to write about Bombay, will try to restrict it as much as possible. This is strictly a travel review, and the ratings is for Mumbai as as travel destination, and Strictly my opinion from what I know about the place.
About the Place
Bombay is the capital of the State of Maharastra, on the west coast of India. Bombay can be described as the financial centre of India, with almost all the big corporates having their offices out there. Its also 'the seat' of the entertainment industry and also the Indian Mafia.
Commuting
Commuting is a breeze in Bombay, you can take the Taxi or the Rick(Auto-RickShaw - A three-wheeled vehicle), which is restricted only to few areas. Both these guys go with the book and never charge you extra, the meter shows some number and they take out a card supplied by the state which describes the rate in rupees for the corresponding meter reading.
The bus service is also good, they even have airconditioned buses, which makes your life easy. Hey, Bombay even has cool cabs, ie airconditioned cabs. But learning the routes of the buses is not easy, ie the number system and all. So I don't know how effective its for tourists who can't speak the lingo.
The most economical way are trains though. The fast and slow trains are in plenty but to get in you should beat the bombaywallahs to it, if you are an alien, you can never get a seat on one of those. You need to learn the trick of the trade you know, ie to jump in before the train stops. But be careful when you do that, lot of people loose their lives on trains. Its better that you get a first class ticket in stead of a normal cos the crowd would be better. If possible, avoid taking young children or women in the normal compartments, they would be crushed to death. Even I was apprehensive couple of times, and the 'stress' is too much, particularly when your station approaches.
Also, pick your train properly ie One day, I got into a train from Mahalakshmi to go to Andheri, and I accidently got into a Virar train. You know, Virar is probably the last stop on western line, and when I wanted to get down in Andheri, the other commuters didn't allow me to get down. They were angry cos I was a Andheri guy who got into a Virar train, their reasoning, there are a lot of trains to Andheri but few to Virar, so avoid getting into Virar trains. I was dissappointed that in the City of Dreams you can't get into the train that you feel like, just because the trains are less you should not take it out on a fellow passenger. I finally got down at Malad.
Shopping & Things to see
What is avaiable in Mumbai is now available in any other major city in India, so I personally feel that there isn't any need to do any shopping over here. If you want to buy some cost effective apparel, visit 'Fashion Street' which is quite popular.
To see,Gateway of India, which is probably the most important landmark, the essel world which is a amusement park, walking around Colaba during the evenings, there is the Borivili National park, Borivili is a sub-urb of mumbai, and you can take a train. There are somemore,but frankly I don't remember all of them.
Food
The place is dotted with Udupi, which is basically south indian, eatries. You can also find normal north indian or the chinese as well. Food is quite good, and in mumbai, you will never starve to death. My breakfast used to be a Samosa or Vada Pav and a green chilli with a cup-a-tea from the local tea wallah near my home, it was near the bus stop as well. The most popular local food is the Vada Pav, basically a potato patty inside some bread. It goes well with anything.
Entertainment & Places to Stay
There are a lot of hotels around, I mean like in all major Indian cities. I found the Orchid special, considering its one of the first 'Green' hotels in Asia. I mean this shouldn't be your worry, you should be able to get a decent acco near the Airport for anything between 3000 to 5000 Rs, depends on your needs and taste though.
There are lots of pubs and discos the likes of Razz Rhino etc, and you can know more if you read the reviews on them on MS, so not mentioning about those.
Things I don't Like
The trains are too crowded, the life is too fast and you don't much care about others. I stayed at Mumbai for 10 months and didn't even know the name of my neighbour, but most of the Udupi hotels are not authentic, when I travel to my office, I see at least 75 people shitting on the rail tracks and on the roads, why can't govt put a big wall on both sides of the rail tracks so that the visitors are not 'repelled' by this.
What I feel
Bombay is a good place, like any other place in India. The people are friendly like in any other Indian City and the food is good like any other city in India. Ie its a normal indian City.
There are couple of good things to see in Mumbai as a tourist, but nothing great. The Travel is ok, but only if you take a Rick or a Taxi, Trains are out of the question and stay away from them if you don't now about them.
All in all, there is nothing special about Mumbai as a travel destination, but there is certainly scope for 1-1.5 days stay if you know the places where you want to go. Thre are couple of Museums and all. There are couple of good places like Elephanta Caves, or Lonavala (which is a hill station) which are near Mumbai. My Advice, do stop over at Mumbai for a day or so in case you are in transit, but don't dedicate a 'holiday' for visiting Mumbai cos you may be bit dissappointed, it would be just like the mad city where you are coming from.
That's It folks, hope you enjoyed it.
Peace
Ranjith