Best to live in? Travel to? Work in? Hard to make a generalization given that each city has its pros and cons.
I lived briefly in Tokyo, have traveled to NYC many times, and visited London only thrice. I'd probably pick London due to the great times I've had there and its proximity to other cities in Europe, as Europe is a favorite travel destination. NYC is a fabulous place but still feels daunting to me at times.
Tokyo is a great place to live; it has great mass transportation system, low crime, cleanliness, and culture. However, the workplace remains very male-dominated and not necessarily the most friendly for western-minded career women. I find that to be the biggest drawback.