"Broadway Baby" was written for the 1971 Stephen Sondheim musical Follies. The musical was not a big success when it first debuted, but it has been successfully revived several times. The cast album is magnificent; Sondheim's songs play very well apart from the shows.

Elaine Stritch did a memorable "Broadway Baby," but there have been other fine babies.

17 November 1985, New York Times, pg. H26:
Elaine Stritch, who brought the house down at Avery Fisher Hall singing a tough, deadpan "Broadway Baby," projects a cartoonish "I've been-to-hell-and-lived-to-tell" attitude that is as dry as the Sahara.

http://lyricsplayground.com/alpha/songs/b/broadwaybabyfolliesthemusical.shtml
BROADWAY BABY
From the Broadway Musical "Follies" (1971)
(Stephen Sondheim)


I'm just a Broadway Baby,
Walking off my tired feet,
Pounding Forty Second Street
To be in a show.
Broadway Baby,
Learning how to sing and dance,
Waiting for that one big chance
To be in a show.