Just spent 5 days in Mumbai with my wife and another couple. We are all British Indians. What a fantastic experience Mumbai was!
Area - We stayed at Chateau Windsor (see Hotel review) in Churchgate. Great location. There is plenty within walking distance and many sites/restaurants are just a short taxi ride away.
Bars - if you don't mind splashing the cash go to Dome at the Intercontinental. Its ranks among one of the most beautiful bars I've ever been to. (NB: Its not the sort of place to visit on a stag do). Shiro at the Bombay Dyeing compound is also gorgeous, but was quiet as we went on a Sunday night. The local area is run down and we were amazed to find such a stunning place in those surroundings.
Traffic - during the day it can take an hour or more to get from South Mumbai to places like Bandra or Juhu. Expect pure gridlock in Mahim.
Beggars - not as persistent as they are in Punjab but still a nuisance in some areas. Most will gratefully accept food. Here is a major tip....in many restaurants we had LOTS of food left over. If this is the case, ask them to pack it up so you can give it to some homeless people on the streets. We did this quite a lot.
Food - Satkars in Churchgate is great for veg cuisine. Swati snacks in Tardeo also good but a bit of a drive from South mumbai. For a more upscale experience Kandahar at the Oberoi is superb. Khyber lived up to expectations - great food, great service and very reasonably priced. Souk at the Taj serves a great Lebanese buffet at lunch. Also, if you fancy a break from Indian try the Mediterranean food at Olive in Pali Hill.
I've got loads more to say but I'm feeling really ill (having returned to England 3 days ago)....I think it was the Indian food at Gaylords on our final night that caused the damage.