Beale Street, in Memphis Tennessee, was a center of black culture, with black owned businesses, black musicians, and black patrons. Letting us know that this love is Beale Street love tells us that the characters in the poem are most likely African-American, but that's no surprise in a Langston Hughes poem.
Love Is a brown man's fist (1-2)
What's interesting here is that the speaker doesn't say "black man's fist." Nope, he says "brown man's fist," which takes the emphasis off race, and puts it on appearances, or skin color. What is the affect of this choice on the meaning of the poem?