https://www.yahoo.com/news/no-evidence-barron-trump-rejected-100000292.html
But . . . . I feel pretty sure that New York University was not his father's first choice. (You don't believe that Barron made the choice of where to attend college, do you?)
It's not a prestigious institution like Harvard, Yale, Stanford, Wharton, University of Virginia, Duke, Emory, etc. It's a credible academic institution. (Hey, I got my Master's at NYU.) Plus, it's in the Village. Cross the street and you're in Washington Square Park where you can easily find a doobie, performance artists who put a can of lighter fluid in their mouths and breathe out fire, or a hermaphrodite without underwear lifting her skirt. (I saw all of that at NYU.) Plus, REAL kids go to NYU, unlike the other schools where rich kids who graduated from boarding schools go. Trump would want his boy to go where the connections to business and politics are. It won't be at NYU.
So, if NYU were the second, third, fourth choice, what would have logically been the first choice.
I think my theory holds up.