The 1923 scenes that were shot in NY are in the Williamsburg and Dumbo sections of Brooklyn. One can distinguish the authentic NY location shots because they contain glimpses of the iconic and recognizable Williamsburg and Manhattan Bridges.
The drunk is rolled on a street in Williamsburg (one site claims South 8th Street) and the Williamsburg Bridge and old Williamsburgh Savings Bank are present in several shots in this sequence.
The familiar poster art was shot in Dumbo (Down Underneath the Manhattan Bridge Overpass) in front of the Manhattan Bridge. Images just like poster artwork are a postcard favorite in the area. Atleast some of the scene containing Bugsy's death were shot here as well--we know this because of the many glimpses we see of the Manhattan Bridge.
Take a look at this link:
http://www.movie-locations.com/movies/o/onceamerica.html-Jon