From experience at an average public high school in NYC, if you get into Binghamton everyone kisses your feet because of how smart you are. If you manage to be graced by acceptance to Baruch or Hunter you’re also a certified genius.
Other than that, people have heard legends of a school called “Harvard” (but where is it?) and probably some D1 college basketball teams, but that’s all.
*Forgot about NYU. Yes, it does have a mystical quality to it among public school kids. I used to be caught up in it.