Bombay. In malls, people wait till you come out of the elevator before getting in. I bet you will not find that in any other place in India.
I grew up in Chennai and currently live in Bombay. I've lived a few months in Hyderabad and Bangalore, and I've visited Delhi a few times. So yeah, I can talk!
Apart from the generally civilized air that is so rare in India, Bombay has great restaurants and malls, easy internet connectivity, lots of clubs that stay open till 1, and some restaurants/clubs that stay open all night. Stay away from the train stations, though. South bombay is calmer than the suburbs and very expensive.
Chennai is hot and the people are rude. It doesn't have anything to recommend itself, except a few startups and beaches. You might run into interesting, smart people around Anna Nagar or Mylapore or the IIT, but it's no use - they don't talk.
Bangalore is full of people in their twenties working in software companies. There are some startups, too. The traffic is heavy, and the weather is the best in India. I interned in Google, Bangalore a long back and remember seeing the road get regularly jammed for several hours in the evening. It's just a pain to go anywhere there. Also, it has no diversity whatsoever. A little like the valley, I guess. It has a lot of clubs, but everyone drops asleep at 10 PM sharp and NOTHING stays open after that.
I don't know a lot about Hyderabad and Delhi. Hyderabad is currently somewhat disturbed by regional issues and has some good South-Indian restaurants. It also has excellent bookstores. Delhi is not safe(at all) in the evenings, and has an AWESOME metro.
As for cost of living, Bombay is crazy expensive, Chennai is dead cheap, and Bangalore, Hyderabad and Delhi are in the middle.
All of these places are overcrowded, noisy and hot. The people will invariably shove you out of queues and counters, stare at you if you wear a hat (or anything that they don't wear), break rules and honk a lot on streets. Welcome to India.