Manhattan around Greenwich Village, Lower Manhattan, Union Square, Chelsea and the Upper East Side looks pretty diverse and integrated. Same for Hoboken, NJ.
Interestingly, NYC was one of the first places where Americans really became integrated (by income and race) in the early 1900s, which fell apart quickly once the rich started moving into "suburbs". Which, at the time, would have been around Central Park and the parts of Queens, and Brooklyn closest to the East River. Though back then the suburbs were still considered urban by today's standards, just not as many tenements.
It's funny though how the slums and tenements of the time are now the exact places that are becoming most integrated and successful within Manhattan.