The “Big Apple” dance became a national craze in 1937. “Governor Wins Praise for ‘Big Appling’”—dancing the Big Apple—was printed in The News and Courier (Charleston, SC) on July 11, 1937. “From the mountains to the seacoast, Southerners are Big Appling” was printed in the New York (NY) Times on July 26, 1937.
 
“Big Apple” became popularized as New York City’s nickname in the 1970s, and “Big Appling” (visiting New York City) has been infrequently used. “Antonia & Pinter Big Appling” was printed in the Daily News (New York, NY) on December 20, 1976.
   
     
11 July 1937, The News and Courier (Charleston, SC), pg. 3-C, col. 2:
SWING IT, MR. JOHNSTON
Governor Wins Praise for ‘Big Appling’
Rock Hill, July 10—(AP): When it comes to dancing. Governor Olin D. Johnston undoubtedly knows his “big apple”.
   
26 July 1937, New York (NY) Times, pg. 7, col. 4:
Big Apple,’ a New Dance, Sweeps Southern States
By The Associated Press.
COLUMBIA, S.C., July 25.— From the mountains to the seacoast, Southerners are Big Appling. The dance is a combination of the old-fashioned square dance and the modern “swing.”
 
28 November 1937, Sunday Herald-Sun (Durham, NC), pt. 4, pg. 2, col. 2 photo caption:
Local Girl ‘Big Appling’ In London
 
Google Books 
American Speech
Volume 13
1938
Pg. 194:
At first dancers are referred to as ‘doing the Big Apple,’ or as ‘dancing the Big Apple’; but soon columnists are writing ‘They Big-Appled,’ or ‘They were Big-Appling.’
     
20 December 1976, Daily News (New York, NY), Suzy column, pg. 12, col. 1:
Antonia & Pinter Big Appling
 
8 December 1984, The Star-Ledger (Newark, NJ), “Voice of Broadway” by Jack O’Brian, pg. 16, col. 3:
It (a musical—ed.) will open in exurban New York Dec. 20, a test of its future Big Appling.
 
4 November 1989, The Morning News Tribune (Tacoma, WA)), “People,” pg. A2, col. 3:
Maurice and Darline Shank will arrive in New York on Saturday for a weekend of Big Appling and then will appear on “Late Night With David Letterman” Tuesday night.
 
Twitter
Jay G.
@Cessna157
Packing up for the commute to NYC again.  Big Appling it again tonight.
9:25 AM · Jul 28, 2010·Twitter Web Client
   
Twitter
KiltedJedi
@kiltedjedi
Big Appling. #yallahguys #JUC6C2016 @ New York City - Laguardia Airport (link: https://www.instagram.com/p/BGrWJn-Jx4o/) instagram.com/p/BGrWJn-Jx4o/
9:45 AM · Jun 15, 2016 from Queens, NY·Instagram
 
Twitter
Michelle Johnston
@Eleytherius
Replying to
@broomedocs
Ha ha. Brilliant! How long are you there? I am Big Appling in a few weeks time.
9:23 PM · Jul 9, 2019·Twitter for iPhone