"Big Burg” is a nickname for New York City (and other big cities) that was popular in the early 1900s, before the “Big Apple” 1920s citations.


(Historical Dictionary of American Slang)
Big Burg n. a big city; (specif.) New York City.—constr. with the.
1918 Stringer House of Intrigue 28: he usually fought clear of the Big Burg.


http://www.hobonickels.org/alpert04.htm
the Big Burg - New York City


15 October 1897, Hornellsville (NY) Weekly Tribune, pg. 4:
Who will be Mayor of Greater New York, is the query that still puzzles the people of that big burg.


10 February 1901, Washington Post, pg. 24:
WE are told with much emphasis that New York is sick of comic opera; that the taste of the public has undergone another radical change, and that comic opera cannot succeed in the big burg, which poses as the center of the theatrical universe.


5 May 1901, Washington Post, pg. 28:
Having been shut out of New York an entire season, Mrs. Fiske has finally secured a theater in the big burg, the Manhattan, formerly leased by William A. Brady.