I enjoy watching old eps of the TV series What’s My Line on youtube (panelists ask yes or no questions to identify a mystery guest). They end with celebrity guests and often a question that’s asked is “Are you in a picture that’s playing on Broadway right now?” What does that mean? Being in a Broadway show makes sense, but a movie? Thanks.
Back then, there were quite a few movie theaters on Broadway. I assume the primary reason was, back then, a movie had to play for seven days in Manhattan as well as in Los Angeles County to be eligible for the Oscars.
The price of real estate in Manhattan eventually reached the point where movie theaters were no longer profitable. It got to the point where it was so hard to find a Manhattan movie theater that the Academy of Motion Picture Arts and Sciences got rid of the Manhattan requirement (except for feature-length documentaries; also, a documentary short subject can be shown in either LA or Manhattan to be eligible).
Thanks, That Don Guy! 
In addition, in those days they didn’t have the sort of saturation booking we have now, where a movie opens everywhere in the country on the same day. Rather, films would usually open first in a few big cities, then gradually work their way around the country. I’ve read about people in the 1950s, who lived in small towns, waiting several months for a movie to make its way to their local theater.
So when Bennett Cerf asked if the mystery guest had a “picture playing in one of the big movie houses on Broad-Way” (which always seemed to be the way he phrased it), this helped to narrow down the time frame. If it was playing on Broadway, it had probably opened relatively recently.