I'm a New York transplant, first got to NYC 13 years ago, been here off and on, but now a longtime permanent downtown Manhattan resident. Perhaps this will sound a little odd, but I go out of my way to befriend native New Yorkers (I'm giving one such native a hard time in the photo, with the typical
"Why me?!?!" response). New York natives are the reason why I moved here in the first place. There is just something about them that makes NYC, well, more authentic NYC. New York-specific accents that don't seem to be going away:

1. Hil-LARRY-ous
2. Hiz-TARA-cul
3. Shtreet instead of street
4. Waiting on line instead of in line (I once asked someone if they were on line and they said, after a puzzled look, yes and that I could go in front of them if I wanted! (It was a long line too).
5. Train instead of subway
6. Even Manhattan itself is said MunHATTAN

I've noticed that if I turn on the accent (it's easy), and add a little Bayside, Queens Italian shoulder shrug here and there, adopt a little Brooklyn Jewish animation, I find that the city makes room for me: on the train, in restaurants, and in general, people automatically give me respect... strange as it sounds, it's absolutely the truth. I turn the accent off and revert to my native nasally Michigan accent, and I'm trampled upon in every way possible. I might as well be invisible.

HOW you say things here in NYC - from my observations - can absolutely alter the kind of experience you have in the city.