1) AAVE's use of Copulas. In most English you form present progressive with a copula and the present participle: I am walking, I am driving, I am working. The copula contains no information on its own. In many languages, a low information word is dropped. In Spanish you say "(yo) soy Americano" meaning "(I) am American." There can be no doubt of the subject of the verb "soy" because it is inflected to match the subject, so the pronoun "yo" communicates nothing in a normal sentence and is dropped. In Russian you take the opposite tack: you say "ya Amerikanets" meaning "I (am) American)" so you drop the copula. You either need the pronoun or the verb to communicate who is American, and in this case the pronoun won. Well in AAVE you drop the copula in those present progressive sentences: "I walking," "I driving," "I working." But then there's an opportunity to put a higher information in all of these sentences: you can use "be" as a copula to express the habitual aspect. "I be walking," "I be driving," "I be working" (usually with emphasis on the "be") mean "I am in the habit of X, but don't assume that is what I am doing at this moment." Degrees can be expressed here: you can replace "be" with "stay" to get more habitual and less present. It's a trip! I'm scratching the surface here but that's a big one.
2) Related: "Needs" + past participle vs "needs" + present participle. I was working with a handyman from Colorado and he said "This sink needs sealed" or something like that. I (Northeast) would have said "this sink needs sealing." Colorado has always had over 50% of the population born outside of the state, so I don't know if that's a thing from there or from wherever his parents are from (not sure and didn't ask).
'mensch' and 'schmuck' are commonly used words in NYC that are not known to people in the South, unless they have studied German (and yes I had to fight capitalizing them.)
Another example... 'they're all' is shorthand for 'they're all gone' in Pennsylvania.
schlep too. To a much lesser extent mishegas and tsuris. There's a continuum for knowing Yiddish words where at one end it's "lived in NYC" and then passes through "had playdates with a Jewish friend" through sequentially "have 1/2/3/4 Jewish grandparents." All of these things possible anywhere in the world, but I agree very much an NYC thing.
Can people here give examples of non-standard grammar or vocabulary (that goes beyond some temporary slang or subculture words)?