I was born in College Point in Queens, NY and moved to Levittown when I was 12. Being of Germanic descent (on my mother's side), I wasn't exposed to the Italian-American "NY accent" but I could definitely be placed as a New Yawkuh.
My college freshman year I went to Cornell and made friends mostly with people NOT from the NYC/Long Island area, which smoothed out my accent to more of a "generic" American from being playfully teased whenever my accent reminded people I was a Long Islander. After returning to Long Island I was much more aware of the accent I previously didn't notice, but I stayed in my "generic" accent. I'd often get asked "where are you from?" when working or out and about.
Since June 2009 I've been in Buffalo, NY for school. I have to say I am truly annoyed by the strong native accent here, but I don't know why. Here, the "r" is strongly pronounced, such that when someone here says "are" it sounds like a pirate saying "argh" but leaving off the "g". I've also noticed that away from the NYC area, the names "Aaron" and "Erin" sound identical, while I've always said more distinction between the "a" and "e".
Language is mutable like genes, but at a faster rate. Outside of rigorous education and training to make one's speech conform to a standard, the spoken language functions as long as it's understood by others. This allows for a degree of variation within a population, like a species able to reproduce with others of its kind. When there's a separation between two populations who speak the same language, little changes pop up that don't get shared, and over time, there's a sort of "genetic drift" effect that builds up into a language separating. For example, a few hundred years ago, English and German sounded alike enough to be dialects or accents of each other.