The rioting began in the Harlem neighborhood of Manhattan, New York after Lieutenant Thomas Gilligan murdered an African American teenager, James Powell near his summer school.

Over the course of six days, the rioting spread to Brooklyn, South Jamaica, and Queens, New York. Later, riots spread to Rochester, New York, Paterson, Elizabeth, and Jersey City, New Jersey, and Philadelphia, Pennsylvania. 

Harlem race riot of 1964 | United States history | Britannica