Unless your family has an extra 200K to burn, or is low enough income that you would get fin aid to match your in-state cost, there is absolutely no reason for you to apply to privates like NYU, or even Ivies, for undergrad. With a track record like yours, I’m sure you will do very well as an undergrad, and then wind up going to a top private or public institution for graduate studies, fully funded. Go where it’s cheap for undergrad. UCB, UCLA, UCSB, UCSD, UCI, UCD. Also U Az for massive merit money, might wind up even cheaper than in-state at a UC for you, what with your national merit status. BTW, make sure you apply to become a finalist, might lead to some additional merit money for you.
I wouldn’t even bother applying to Cornell, NW, or NYU. What are you gonna do when they accept you, and your parents have to pay 85K/yr for you to go there, as opposed to 30-40K for the Az or in-state options? And for what? You’re gonna wind up at the exact same places for your PhD as you would have, coming out of one of the UCs with excellent undergrad physics, or U Az on the cheap, too.
Seriously, you’re lucky in that you already have found something you love, that you’re good at, and you’re in a state with at least five highly ranked programs for it at large public universities where, if you decide you want to study something else, they offer tons of other majors. Save yourself the stress and the expense of applying to the highly selective privates which don’t offer merit money, or where you’d be unlikely to get merit money. Talk with your parents about it, and hear the relief in their voices as they tell you that they’d have been willing to pay for you to attend a private at rack-rate, but that they’re very happy that you can get a wonderful undergrad education at much lower cost at an in-state private, or at U Az.