Brooklyn did this. They were street performers playing for change in NYC. Hedwig and the Angry Inch was supposed to feel like a low rent stop on a nationwide tour.
Yes, Little_Sally, La Chiusa's Wild Party was presented as Vaudeville sketches, with signs announcing the next act and everything.
Would Chicago count? The whole show is set up like a series of vaudeville acts.
And I might be wrong, but I always considered 42nd Street to be a borderline traveling show, especially with the end of Act I and how the audience becomes the 'Pretty Lady audience' thanks to Julian Marsh's announcement.