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.
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.
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.