Green’s Dictionary of Slang

Avenue, the n.

(US) Broadway.

[US]G. Bronson-Howard God’s Man 371: The activities of the Petties take in the ‘Avenue’ as well as the ‘Lane’.
[US]G. Fowler Schnozzola 37: All my life had been lived in Harlem and Coney Island and Lower Manhattan, never on the Avenue except to walk on it. By ‘Avenue’ Durante meant Broadway.

In phrases

on the avenue (US black)

1. lit. in the street.

[US]C. Himes ‘Prison Mass’ in Coll. Stories (1990) 154: Well, where did he think you were going, down on the avenue?

2. in general use, from a mass point of view.

[US]J. Wambaugh Choirboys (2007) 216: He likes to run because he’s a celebrity on the avenue.
D. Flamming Bound for Freedom 324: It was common gossip on the avenue that Sam Baumann [has] moved bag and baggage into Fred Roberts’s camp.