Hi,

I have a base in India, thus I write. I would suggest going to New Delhi. It offers a blend of modern and old. You can also visit the world famous Taj Mahal, which is close by to Delhi (either by Train or Car).
Delhi offers several sightseeing options, e.g. The Red Fort, The Qutab Minar, The India Gate, The Lotus Temple. It also provides good accomodation, e.g. Sheraton, Hyatts, as well as leading Indian Hotels.

Finally, you could also visit the desert state of Rajasthan, which is close to Delhi.
Rajasthan has several sights to see as well, and is a very cultural/beautiful place.

As for Bombay, it is like New York, a cosmopolitan city. It has a few sightseeing options, and several hotels, nightclubs, restaurants, shops.

It all depends on how many days you want to spend in India, and what you are looking for. Overall, I recommend Delhi, since it offers sightseeing, culture, nightclubs,great food,proxmity to other locations,and shopping.

Let me know if I can help you any more.
Best of Luck,
AK