I lived in New Delhi for six years and travelled to Mumbai several times, but not since 1997, so my advice is obviously dated.
Kyber was not only one of the best Indian food restaurants in India, it was also one of the best looking and most interesting. It would be my top recommendation if it still exists.
China Garden was the top Chinese restaurant and the gathering place for the Bollywood movers and shakers but I have no idea if this is still true. It's owner, Nelson, was a local legend.
The fine dining (i.e Western-style food), restaurant in the Oberoi (not the Oberoi Towers, which is next door and not as nice) was very good as well.
I never ate a one of their restaurants, but you must visit the Taj Mahal Hotel on the waterfront, if only because of its historical significance. It was probably the first first-class hotel in India, was actually built backwards (the front door is in the back) and was the site of John and Oko's first bed-in. It's an architectural classic, and I bet the top restaurant in the hotel (hotels of that class in India usually have at least 4 or 5 restaurants) would be great as well.
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