There are a ton--what kind of role are you auditioning for? I assume you mean any Broadway show, not just a musical (in which case the Paul Chorus Line monologue is the only one that jumps to mind).
Comedic? Dramatic? Shakespearean? Classic? Modern? Age range? What show are you auditioning for? Etc., etc., etc.
There are lots of great "broadway monologues". Start off with a trip to the bookstore or the library and look through the various monologue collections. -And there are even some websites with monologues.
Bobby's search for the girl in the motel room - but, the real punchline does involve another character. Paul's speech in A Chorus Line however is the first one I thought of.