The Times has visualized the change in the ethnic break down of the City by census tract. Here is the map for Black New Yorkers:
The map text from the Times:
Canarsie, Brooklyn, had one of the greatest increases in its share of black residents in 2009 (to 81% from 67%), while recently gentrified neighborhoods like Prospect Heights, Clinton Hill and Fort Greene saw double-digit decreases.
See the rest of the maps here.
There is also an accompanying article Region Is Reshaped as Minorities Go to Suburbs:
Metropolitan New York is being rapidly reshaped as blacks, Latinos, Asians and immigrants surge into the suburbs, while gentrification by whites is widening the income gap in neighborhoods in Manhattan and Brooklyn, according to new census figures released on Tuesday.