“Fun City” is a New York City nickname that originated with Mayor John Lindsay (1921-2000) on his first week in office in January 1966. The nickname was satirically used and quickly lost popularity after “Big Apple” became popular in the early 1970s.
 
The “Fun City” nickname still lives on in the “Fun City Bowl,” an annual charity football game between New York’s “Finest” (New York Police Department or NYPD) and New York’s “Bravest”  (Fire Department of New York or FDNY) that was first played in 1973. Locations for the Fun City Bowl have included Downing Stadium (Randall’s Island), Hofstra Stadium (Hempstead, Long Island), Shea Stadium (Queens) and MCU Park (Coney Island).
 
 
4 May 1974, Newsday (Long Island, NY), “Preview,” pg. 9A, col. 2:
FOOTBALL GAME. Next Saturday. The New York City Police Officers vs. New York City Firemen at Downing Stadium, Randall’s Island at 8 PM. A pre-game show is scheduled for 7 PM. Proceeds from the “FUN CITY BOWL” will be distributed to the families of policemen and firemen who died in the line of duty. $4.50 at Ticketron.
     
22 May 1976, New York (NY) Times, sec. 2, pg. 14, col. 2:
FOOTBALL
Fun City Bowl, policemen vs. firemen, at Hofstra Stadium, Hempstead, L.I., 8 P.M.
 
19 May 1977, New York (NY) Times, pg. D21, col. 1:
Finest to Tackle the Bravest
There will be a football game played at Shea Stadium on Sunday. Yes, a football game.
 
In the midst of the controversy of the Mets’ refusal to allow the Jets to play at Shea during the baseball season, the stadium’s prime tenants have given permission for Fun CIty Bowl V to be held there Sunday.
 
That is the name of the game matching teams from the Police and Fire Departments called, respectively, New York’s Finest and New York’s Bravest, and they will play tackle football.
 
The game, which in previous years had been played at the Hofstra Stadium in Hempstead, L.I. is a charitable one, with proceeds going to the Burn Center of New York Hospital-Cornell Medical Center. Tickets are priced at $5 and $2.50.
 
6 May 1979, Newsday (Long Island, NY), “Finest vs. Brave Bravest=Mostest” by Bob Herzog, Leisure sec., pg. 4, col. 3:
The Finest vs. the Bravest. Nothing subtle about this football rivalry. No sir. It’s the New York City cops (Finest) against the New York City firemen (Bravest) in the Fun City Bowl. This year’s seventh renewal is scheduled for 8 PM on Friday, May 18, at Hofstra Stadium and a crowd of 10,000 is expected. But it had more humble beginnings.
 
The idea grew out of an argument on a cold, wet November night in 1972 between Joe Laughran, then a New York CIty policeman, and Robert (Pudgy) Walsh, a lieutenant with the New York City Fire Department. The two friends were debating—rather heatedly—the merits of their respective jobs. Walsh had founded the successful Brooklyn Mariners semi-pro football team, which included several cops. Loughran needled Walsh that the Mariners couldn’t win without them. Walsh snickered. A rivalry was born.
 
Daily News (New York, NY)
NYPD and FDNY brawl during charity football game ironically nicknamed ‘Fun City Bowl’ (WARNING: GRAPHIC LANGUAGE)
BY JULIAN GARCIA
Monday, May 23, 2016, 1:09 PM
(...)
It happened again on Sunday, when the city’s Bravest and Finest squared off in what was supposed to be a charity football game at MCU Park on Coney Island. Instead, it turned into an all out brawl that resulted in some bloody faces, bruised knuckles and soaring testosterone levels.
 
In video shot on the field just after the cops’ 29-13 win over the firefighters at the iconic Brooklyn ballpark during what is ironically nicknamed the “Fun City Bowl,” the teams are seen converging near the 50-yard line for what was supposed to be a traditional post-game handshake. But tempers flared as players got in each other’s faces.