The city of Binghamton, New York, is sometimes nicknamed “Bingo.” Most likely, the nickname is derived from the “bing” in the name “Binghamton.”
 
Binghamton had a baseball team in the 1880s, and it was often called the “Crickets.” The Binghamton (NY) Leader newspaper called the team the “Bings,” “Bingos” and “Bingoes” since at least the 1887 season. “Bingos” was cited in the New York City magazine Puck on July 27, 1887, in an item from the Binghamton Leader.
   
The Evening Leader (Wilkes-Barre, PA), on July 30, 1887, hinted that the term might have been coined by Charles McCormick of the Binghamton Leader:
 
“The following report of the game, in view of Wilkes-Barre’s experience there yesterday, may be of interest to the readers of the LEADER. It is by Charles McCormick, the funny ball man of the Binghamton Leader. He says: The Bings went up to Rochester yesterday and the ‘Lushers’ just breathed on them. They became intoxicated forthwith, and “Bob” Barr went into the box and began putting little geometrical conundrums to them, and they all got mixed up. When the Rochester players gather around a “Barr,” they feel at home, and they become merry and chipper immediately. Casey was the only Bingo that succeeded in stepping on the disc.”
   
   
Wikipedia: Binghamton
Binghamton /ˈbɪŋəmtən/ is a city in, and the county seat of, Broome County, New York, United States. It lies in the state’s Southern Tier region near the Pennsylvania border, in a bowl-shaped valley at the confluence of the Susquehanna and Chenango Rivers. Binghamton is the principal city and cultural center of the Binghamton metropolitan area (also known as Greater Binghamton, or historically the Triple Cities), home to a quarter million people. The population of the city itself, according to the 2010 census, is 47,376.
     
27 July 1887, Puck (New York, NY), “After a Base-Ball Game,” pg. 361, col. 2:
The stars came down from their lair yesterday, and the Bingos went out upon Stowe’s Flats with the intention of kicking the stuffing out of ‘em; but instead, they knocked several qualities of bailed hay out of the Bingos.—Binghamton Leader.
 
30 July 1887, The Evening Leader (Wilkes-Barre, PA), pg. 4, col. 5:
The Bings and the Lushers.
The Binghamton club went down before the Rochesters on Wednesday by a score of 4 to 1. The following report of the game, in view of Wilkes-Barre’s experience there yesterday, may be of interest to the readers of the LEADER. It is by Charles McCormick, the funny ball man of the Binghamton Leader. He says: The Bings went up to Rochester yesterday and the “Lushers” just breathed on them. They became intoxicated forthwith, and “Bob” Barr went into the box and began putting little geometrical conundrums to them, and they all got mixed up. When the Rochester players gather around a “Barr,” they feel at home, and they become merry and chipper immediately. Casey was the only Bingo that succeeded in stepping on the disc.
   
26 August 1887, The Evening Journal (Jersey City, NJ), “Base Ball,” pg. 3, col. 3:
“The Bingos have gone up the flume. We don’t know what the flume is, but we do know that the Bingos have ascended something via the back stairs. (...)”—Binghamton Leader.
 
23 August 1888, The Evening Leader (Wilkes-Barre, PA), “Base Ball Briefs,” pg. 4, col. 3:
The Central League has criminally neglected to pass any resolutions of respect and condolement for the deceased Bingos.—Binghamton Leader.
 
29 May 1893, Wilkes-Barre (PA) Times, “Base Ball Notes,” pg. 1, col. 3:
The Bingo management has signed Mike Slattery, released by Wilkes-Barre. His many friends in this city will be glad to see “Old Boy Slat” taking care of his old bailiwick in his center garden. “Slat” couldn’t get the hang of the mines or the coal heavers, and he is glad to get back to old Bingo.—Binghamton Leader.
 
NYS Historic Newspapers
19 February 1895, Elmira (NY) Gazette, pg. 6, col. 4: 
BINGO’S TROUBLES.
Binghamton, N. Y., Feb. 18.—J. H. Roberts, representing a majority of the stockholders of the Binghamton Woolen Company, appeared before Judge Parker this morning and presented an order to show cause why the affairs of the company should not be closed up.
 
Old Fulton NY Post Cards
31 May 1895, Owego (NY) Daily Record, “Local Record,” pg. 3, col. 1:
Score two for Bingo yesterday and both against Elmira. Morning at Elmira Bingo, 16, Elmira, 13. Afternoon at Binghamton Bongo, 11; Elmira, 3.
 
20 January 1897, Elmira (NY) Daily Gazette and Free Press, pg. 7, col. 4:
JUST LIKE BINGO.
Binghamton papers enumerate among the charities of that city the permission given to the poor to take away the charred sticks and timbers of the burned court house, adding that it “saves, at the time, the expense of clearing away the rubbish.” Ah, yes.—Susquehanna Journal.
 
Chronicling America
23 August 1919, New York (NY) Tribune, pg. 10, col. 3:
A Double by O’Rourke
Wins for the Bingoes
BINGHAMTON, N. Y., Aug. 22.—...
   
Google Books
Baseball Team Names:
A Worldwide Dictionary, 1869-2011
By Richard Worth
Jefferson, NC: McFarland & Company, Inc.
2013
Pg. 37:
Binghamton, New York
Bingoes 1885 New York States (ind.); 1888 Central (ind.); 1892-94 Eastern (ind.); 1901-17 New York State (B); 1918-19 International (AA). Tag was a monitor used for headlines, i.e., “Bingoes edge Stars, 4-3.” The name was also spelled Bingos. Newspapers, i.e., the Binghamton Daily Leader, sometimes contracted the name to Bings. In the nineteenth century “bingo” was baseball jargon for a “base hit.” The term is related to the numbers game of “bingo.”
     
Google Books
Bud Fowler:
Baseball’s First Black Professional
By Jeffrey Michael Laing
Jefferson, NC: McFarland & Company, Inc., Publishers
2013
Pg. 89:
The 1887 season found Bud Fowler back in the east playing for the International Association’s Binghamton Bingos (the Binghamton franchise was also referred to as the “Crickets” which was a long-term designation).
 
Ramblin’ with AM
Saturday, June 10, 2017
Local Saturday - And Bingo Is Our Name-O
(...)
He was looking forward to an explanation of why one of the nicknames of Binghamton, New York, a small city upstate where I work, is “Bingo”.
(...)
One blogger said the Bingo nickname came from an early 20th century marketing campaign.  But I knew there was a minor league baseball team in Binghamton called the Bingos, and they were playing as early as 1885.  This online article describes their 1887 season.
 
Twitter
Rebecca O’Brien
@1976baby
Just read an article where they claimed Binghamton is referred to as “Bingo”- I have NEVER heard or read that in my life.  @BinghamtonNow
10:36 AM - 23 Aug 2018