International student chances for NY colleges

Is just that my aunt is living in NYC and I would like to live near her, in NYC or at least the state, since I have no one else known there.
Living in New York is also one of my dreams.
Would you recommend me replace Hamilton for Lafayette?
I like Colgate, but I don’t know if I would have more chances there or in Hamilton, even though they are small in both of them.
Universities looking for diversity would enhance my chances, I’m sure, since I’m Hispanic at the same time I lived many years in Europe.