Go to FSU. It’s not worth the debt, which your parents would have to shoulder - don’t do this to them.
Do all you can to establish yourself at FSU - strive to be the best there. See if you can get a paid internship in anything in NYC summer after junior year (meaning positioning yourself well and reverse charting your path so that August before junior year you can apply and thus doing everything right your fest two years).
Then get your graduate degree from NYU. NYC isn’t going anywhere.