The mirage tmnt, aren't so much new york it's more from the perspective of a subburban Massachusett white young adult comic geek's perspective of what a new yorker is like.
Realistically the tmnt culturally would be Pseudo Shinto Buddhist, learn to speak write and read in English and Japanese, would be raised as trained killers in the art of ninja, but in their spare time would copy off of black american culture from what they observe from the storm drain or exploring the above ground in the 13 or 15 years of them being mutated into hominid anthropromorphsized intelligent creatures and anti social pop culture geeks learning human culture from watching stolen cable tv and would only be preceived as being white coded once they started interacting with April O'Neil and Casey Jones making them apart of their surrogate family of misfits in universe.
Eastman and laird were inspired by copying and parodying off the characters in the media they consumed such as the death wish franchise, dirty harry franchise, cheesy sho kasugi franco niro canon ninja flicks (terrible movies where you have white guys with mustaches with headbands with ninja logos on them, doing summer saults and katas defending or trying to steal some japanese mcguffin or they have a japanese rival.*) and the dialog straight out of racist comic book artist & writter Frank Millers weeb tropes such as turing batman and daredevil into hardened ninja or zatoich when they use to be just brawlers that knew some boxing karate or judo but wasn't straight up given the frank dux james bond esque backstory, turning wolverine into a Ronin Samurai fighting abunch of hand ninja in romances or being a bastard baby daddy with multiple japanese chicks native american chicks and red headed white women, his lone wolf and cub series, and ronin holy terror or 300 with his fascist, anti black racist, & islamophobic commentary. So to the readers of the original mirage turtles you can see yourself and preceve whatever representation or race coding you can self imagine on what the turtles could be because their frank miller & jack kirby parodies and their fictional anthropromorphsized turtles..
Now on the comments about Asian and whites representation in mutant meyhem, asians and whites aren't the dominant representation of ( 1980s new york, 1990s new york, 2010s or 2020s new york culture .*) Whites jews Arabs and Asians practice hip hop culture and some try to speak in a new york blacksent, some asians east indians arabs act like white or jewish peers and delinate from their culture or thick accents to assimilate into whiteness, whilst others appropriate black culture to fit in, in what it means to be an american citizen. The 1987 show, 1990 film, 2003 show, 2012 show introducing and portraying Michaelangelo or the turtles in general with a suburban California surfer bro accent and lingo isn't the culture of a child growing up in new york borrows.
Tmnt is ingrained into the fabric of hip hop culture and could be precieved as black coded since the 1987 cartoon have the turtles participate in teen culture of the 80s like use black american slang, dress in punk rock (which was started by black metal heads) house hiphop and r&b music fashion and out side of dressing like Brooklyn jewish super hero ben grimm the thing of the fantastic four civilian clothes or homeless power plant worker Ohio spring wood slasher Freddy Kruger (trenchcoat and fedora) and raph often portrayed speaking in a brooklyn accent started by the 1990s film and 2003 show incarnation, the turtles are seen dressed in the 2003 and 1987 in period appropriate hip hop fashion in some of their desguises, b boying to a ghetto blaster, in their live stage performance Michaelangelo raps and sings new jack swing type music in out of their shells tour.
The tmnt live in a bomb shelter sewer lair underneath a low income area lower eastside with street crime running rampant caused by gangs like the purple dragons who are a mixed gang of black white and asian street criminals, the turtles would realistically observe culture from black americans, Caribbeans, Cuban, Puerto ricans, Dominican teens and would most likely pick up accents slangs fashion and behavior from new yorks predominant black american culture, if tmnt took place in a earlier time like the 1930s & 1940s golden age of comics with Harlem Renaissance black excellence, or mafia gangster culture was prevelantly they would've taken on a goomba Italian jewish russian irish culture ("batman long halloween comics for example portrays a gotham city stuck in the 1920s 1940s speakeasy gangster culture ." *)
