Watching people in their natural habitat is one good way of getting a grasp of a city's character, especially in a big city such as New York. There's a subtle art to it, I think, and one must do it in as an unobtrusive and less creepy manner as possible. Nonchalance while snapping a picture of them would also help you from not getting accosted or getting rude stares.
People watching, or technically naturalistic observation, has a following already. Wikihow has beginner's guide on how to observe people, and even New York Times had a piece about the practice.
pics, from above: lovers check out the pictures they have taken in Central Park; a tourist snaps a picture in busy Times Square; an Abercrombie & Fitch employee entertaining a would-be customer; an old lady in Museum of Modern Art grounds.