meh buffalo is not a flagship. you are fine.
I am from NY and there isn't really a clear one, like CT or MA.
you'll never convince a NY-based college sports fan (the few that exist) that their allegiance shall be to Stony Brook, Albany, or Buffalo. The schools THEMSELVES don't even care about their teams, why the heck should NY residents?
This is why everyone, even private Universities, keep up the marketing/advertising battle for ownership of NY... I remember there was once an aggressive Syracuse athletics ad campaign around NYC in subways and on taxis, not sure if it's still around. Syracuse is NYC's team? really? lol sit down. Most of Metro NY can't even find Syracuse on a map.