This is the same question that I had argued with a Native American Teacher here in Italki.
New york is a state, it is not called big apple. New york is a city it is loccating in the Sate of New York. A lot of teachers from Australia whom they wrote in support the American teacher, including Jura in favor that New York is called big apple. The correct answer that we compromised is new york new york.
Amanda's answer is NYC, which is New York city. She does not mean New York state, I go for her answer. Precisely, the correct anser is new york new york. Which means New York City in the State of New York. NY is for State of New York and NYC is for New York City.