I don't know how old you are, maybe you've got better info than I do about America in 1962. I wasn't aware of much in 1962, but by the time I could read newspapers in the late 1960s, there very definitely were "no-go zones" for white people in America.

And substantial portions of America were still "no-go zones" for non-white Americans, and had been for generations. You might want to look into the term "sundown town".