“Big Apple” date?: January 15, 1920
It is probable (although not certain) that we have almost the exact date for the "Big Apple" utterance by the New Orleans Fair Grounds stable hands. New York (NY) Morning Telegraph track writer John J. Fitz Gerald (1892-1963), who popularized "Big Apple" as his catch phrase in his 1920s columns, wrote in a column on December 1, 1926 that he had met Jake Byer at the Fair Grounds when the "Big Apple" conversation happened. I found this piece of the puzzle, identifying both Fitz Gerald and Jake Byer at the Fair Grounds in January 1920. From the New York Morning Telegraph, January 15, 1920, page 3, column 1:
J. J. Fitz Gerald has sold the 3-year-old colt Dunsandel to J. Byer and the aged plater Onwa to G. R. Allen at private terms. Allen will ship Onwa to Tia Juana to-night.
J. J. Fitz Gerald has sold the 3-year-old colt Dunsandel to J. Byer and the aged plater Onwa to G. R. Allen at private terms. Allen will ship Onwa to Tia Juana to-night.