My daughter was undecided as to major when she entered undergrad. She was leaning toward linguistics but was cured of that after she took a class in linguistics her first semester. NYU was not affordable. My daughter attended Barnard, which provided her with need based aid of almost the full cost of tuition. For grad school she attended NYU Wagner and got a degree in nonprofit management. She is not fond of NYU – when she attended as a graduate student, it made her very happy that she had attended a different school for undegrad. She was very frustrated by the bureaucracy & indifference of administrative staff at NYU. (On the other hand NYU gave her a very big diploma which she has framed on a wall on her office … I suppose that counts for something).
Don’t take on debt you can’t manage for your son’s undergrad – that is only 4 years of his life that will go by very quickly – and afterward he will move on wherever he goes and you would be left with the debt. If he does go to grad school, the graduate degree is the one that will matter more --although truthfully most employers don’t care about the college name.