For what you are talking about, American English doesn't really have a formal and informal 'you'/'your' -- any variations of it are almost exclusively dialectal/regional. (Though, arguably, exposure to more diverse media has shifted this over the years.)
The short answer for those who don't want to read my nonsense:
You can use it that way, but it's likely to be read as an accent [in my experience] no matter what you do. Other variations of 'you' would include ya, yah, and yeh. (I would personally go with yah or yeh because 'ya' can also be a shortened version of 'yeah.')
Long answer:
New Yorkers, Southerners, and Bostonians usually have the strongest/most recognizable accents/dialects, and because of that, readers will likely 'hear' what they expect in the text. Then there are hundreds (if not thousands) of other different accents/dialects that can boil all the way down to a town or community, such as rural farm towns and more urban neighborhoods, or even different generations. There is no real neutral accent/dialect of most languages, but most have a Standard/Broadcast 'accent' that's widely used in media.
So I guess the better question to ask is, if she's not supposed to be a New Yorker, what is she supposed to be? If you can answer that, you can probably find a video with examples to help you out.