Yes, the problem is, you may be admitted to some of the less-competitive preppy private schools but your stats wouldn’t get you merit scholarships for free tuition. These schools often have a 70k+ price tag per year. Scholarships will go to those students way up in the top percentiles (in terms of stats or other achievements).
I usually don’t give this kind of advice (because your feelings are your feelings, and disappointment is hard to take, especially when you’re young) but try to feel very, very grateful for the possibility of graduating debt-free from Rutgers. With the whole country and economy in disarray these days and many people losing their jobs and investments, many students will be forced to go to less expensive options than they had planned, and many more will now be hard-pressed to attend college at all.
Hope it works out for you. The college you attend does not have to define your life; it’s what you do while you’re there.