I am pleased to see this book is being read, since it is one of my favorite Baldwins.
The story takes place in New York City, and I am guessing it takes place in the late sixties or early seventies because Tish's father was coming home from the Korean War when he met her mother. The book was first published in 1974, which is not necessarily a clue, but in this case, probably is.
So what does that have to do with Beale Street? This is a street in Memphis, Tennessee. There still is a Beale Street there, to this day. Beale Street was particularly important in the Twenties for a few reasons. This was during Prohibition, and there were a number of speakeasies on the street. There were also gangsters around and about, including Machine Gun Kelly. This was also a bit of a "red light district," where prostitutes were available. But most important was the music offered at the Beale Street establishments, with world-class musicians playing blues and jazz. There is a famous song called "Beale Street Blues."
I would say that Baldwin wanted to evoke the idea of the blues of the African-American experience, whether in New York or in Memphis, Tennessee, both as music and as a commentary on the difficult lives of African-Americans.