NYU is indeed lousy with financial aid, but they’ve been known to be generous with exceptional candidates whom they want to attract. Apply just to see what package they offer, being ready to walk away if it’s insufficient.
BTW, do you have your fee waivers? Both for ACT and SAT tests, and for application?
Don’t pass on Williams just because you’re afraid of gen ed… in fact most great math programs will have gen eds too.
If you intend on specializing in math, for example, a fairly high level of French or Russian is required. Philosophy has Logic classes that would likely be of interest and would enrich your thinking. Working with algorhythms in CS will also help you think differently. And you can’t truly be educated if you can’t write well (Freshman seminar) or have no clue about the rest of the world. This is a fundamental principle at most American universities.
If you truly want to do math and nothing but, apply to UK universities, where your program (“course”) is strictly the subject for which you were selected. Use the UCAS website. Look into Oxford, Cambridge (choose one and have everything ready by October), plus Durham, Warwick, Imperial, St Andrews, Edinburgh. Look carefully at each “course” since the classes will be prescribed and required, but will differ from university to university.
Since you’re very young, another option for you would be to hold off graduating early and attending high school in a country with a very advanced math curriculum and STEM academies. However, you’re advanced enough that even Further Maths at A-Level wouldn’t be that useful.
Finally, there’s USC’s “early college” program.