According to the "Big Onion" people, long before it was called "the Big Apple," people who knew New York called it "the Big Onion." I asked them simple questions. Who said this? When did they say it? Do you have any historical citations for "Big Onion"? I wasn't given anything.
The New York Times is completely digitized. A search for "big onion" in the Times and in the digitized Brooklyn Eagle turns up not a single citation.
The walking tour company is about the only place you'll see "Big Onion." It's a good walking tour company -- with a bad name.
Only one relevant hit shows up on the millions of digitized pages of Newspaperarchive.com. As you might have guessed, the use is post-Big Apple:
27 December 1986, Frderick (MD) Post, pg. A-8, col. 4:
These and other tidbits are revealed in Sharon Churcher's new book, "New York Confidential," which refers to the Big Apple as the Big Onion.