As others have noted, there are many different New York accents. I’ve even known people who were born and raised in Manhattan, yet spoke perfect middle-American English, without a trace of New Yorkese.
And I’m surprised how alike many NYC-area accents were to that of my grandma’s, born and raised in a very desolate Southern Utah area: “fetch some erl,” “light up the erl berler,” “the reserver water is low,” “do the warsh,” and many, many other similar terms and speech.
My best lay-girl guess: her mother was from Amsterdam, pop from County Cork, Ireland. Since the Dutch and Irish were amongst the major settling Eastern colonists, her speech probably hailed from the shared East Coast origins. There are some interesting websites that identify a general Utah accent and claim that there is a Southern Utah English that is unique in may ways.
I live close enough to NYC that some pronunciations and word use are very “New York”–distinctions between "Harry " and “hairy,” drinking soda and standing on line…but most people here do not have that outer borough accent. A few do, though, which leads to this story:
Me (consulting in a school): So what can you tell me about your student Jimmy?
Teacher, a transplant from Brooklyn: Well, he struggles a lot in reading and math, but you knew that already. He has a lot of friends, and he’s incredibly autistic–
Me (shocked, as Jimmy does not appear to be anywhere near the spectrum from where I sit ): Autistic? Really? (Pause, then) Ohhhhh…