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:
New York (state)
There are 62 cities in New York. The largest city in the state and the most populous city in the United States is New York City, which comprises five counties (each coextensive with a borough): Bronx, New York County (Manhattan), Queens, Kings County (Brooklyn), and Richmond County (Staten Island). New York City is home to more than two-fifths of the state's population. Albany, the state capital, is the sixth-largest city in New York State. The smallest city is Sherrill, New York, in Oneida County. Hempstead is the most populous town in the state; if it were a city, it would be the second largest in New York State, with over 700,000 residents.