Apologies in advance for my cynicism, and I would love to be proved wrong, but I believe the legacy bump doesn’t exist at highly selective schools for those who need financial aid. I would only REA Yale if you are sure top nonhooked admits from your school get admitted there.
Princeton is a very tough admit for math. And an even rougher major if you do end up going there.
There is a preponderance of prospective CS major at most places. Be conservative with your list if that’s the priority.
Your school appears long on reaches and short on safeties (if there is such a thing as a safety these days). Ivies and other elite schools turn away 10 qualified students for every one that they accept, so as strong as your record is, admission to Yale, Princeton or any Ivy is a long shot. To make matters worse, CS is about the most competitive major at schools with strong programs.
Your list seems focused on the Northeast. Why aren’t other highly ranked math programs in the region like Brown and NYU on your list? Would you consider schools in other regions? Several Big10 schools - UofM, Purdue, UW Madison, Penn State and UIUC are strong in math/CS.
If budget is an issue, you may want to look at honors colleges within less prestigous schools - think top 100 vs top 20. Honors colleges offer several perqs: preference for class registration, greater access to professors for research, their own dorms (sometimes), healthy merit awards (usually), and prestige beyond their host universities. As others have mentioned, less prestigous schoos with strong programs like Alabama are buying top students with financial aid. We have friends whose kids were outstanding students (think Northwestern caliber) and they landed at THE Ohio State because of the generous packages offered.
I would recommend applying EA wherever it is available. Acceptance rates at most schools for EA applicants are higher than those for RD at most schools. You get the added bonus from hearing back early and being done with the stress of college admissions.
I know this sounds nuts, but your 780M score might still be low for top CS programs. For admitted CS students at CMU, the 75th percentile for math is 800 and the 25th percentile… wait for it… is 800. I would not be surprised if MIT is throwing up similar stats. And with your demographics you will need to be toward the top of the standardized test score range.
The Chancellor’s Scholarships at Pitt are one example. They are also extremely competitive, but that is sort of the point–they are competing for students with places like Yale.