The title of this movie is a mistake. The impoverished immigrant neighborhood of New York City at the time, where much of the movie takes place, and to which the title refers, was the Lower East Side. This was located in a section of the east side of Manhattan Island. It therefore would be west, not east, of the river. (Though if you really wanted to stretch the point, it could be argued that it is indeed east of the river--if the river in question is the Hudson.)
Marjorie Rambeau's Italian accent is so shaky that, after the graduation ceremony, she tells a well-wisher "Gracias" ("thank you" in Spanish) instead of the Italian "Grazie."