Big Apple
"The Big Apple" was popularized as a name for New York City by John J. Fitz Gerald in a number of horse-racing articles for the "New York Morning Telegraph" in the 1920s. The earliest of these was a casual reference on 3rd May, 1921:
Home Run Apple
The Home Run Apple is a motorized apple prop in the batter's eye at Citi Field in New York City, New York, United States; which rises whenever the New York Mets score a home run there. The original, smaller apple was first installed in Shea Stadium in 1980 at the behest of Al Harazin with a replacement being installed at Citi Field upon that stadium's opening in 2009. The original was tall while the replacement is tall and wide.