Yes. This is a tough issue. There are plenty of people who could spend $90,000 or more per year for a bachelor’s, but who find this to be difficult to afford and also difficult to justify. It can be very hard to decide between spending the big bucks at a famous university versus a more affordable bachelor’s degree at an in-state public university (and you have quite a few very good ones in New York).
I also have some doubt regarding whether a bachelor’s degree is worth paying full cost at a private university. You could very well end up spending more than $90,000/year for university. I thought that Tufts was already past that point, some others on your list are close, and costs will increase from one year to the next. I would expect that $400,000 for four years is entirely possible. This of course does not address the additional issue that many students take longer than four years, and a dual degree is one reason for some students to take longer than four years. Unfunded graduate degrees are also possible (such as a master’s degree).
I think that you need to set a budget as soon as your reasonably can. Your daughter might very well end up with a full pay acceptance to Yale, Tufts, and several SUNY’s, and I do not think that you want to be arguing and wondering about whether it is worth the cost in April. Assuming that you set a budget that is significantly higher than the full cost of attending a SUNY in-state, you might want to also decide whether any money not spent for undergrad would be available for graduate school.
I did go to an expensive (and stressful) famous private university for my bachelor’s degree (as a math major), and then went to an expensive famous private university for my master’s (in a sub-field of applied math). In graduate school I found myself studying alongside quite a few students who had attended and done very well at less expensive public universities, in many cases including their in-state public flagship. With a bachelor’s from a public university my fellow graduate students still got their master’s, in a sub-field of math, at a highly ranked private university (Stanford in this particular case). The rest of my immediate family has success at attending the affordable public university for their bachelor’s degree, and then the highly ranked university for their graduate degree.
I do not generally think of Yale as “low stress”. However, attending a highly ranked university, or maybe any university, might be stressful for one student and not as stressful for another. At least to me the most important thing for a student who attends a highly ranked and academically demanding university is that they need to want to do it. The desire to work hard needs to come from inside the student themselves.
Regarding music and math, I think that a student can major in math and also take the music classes that interest them. This would suggest that your daughter might want to attend a university that has the music classes, but probably does not need to complete a dual major.
I am hard pressed to think of any schools to suggest that aren’t already on your list and would be preferable to a SUNY without being expensive. U.Mass Amherst is very good for both music and math, and has some merit aid for out of state students, but is large. McGill is similarly very good for both music and math, but again is large and is known for grade deflation, which could be stressful. I sometimes get Amherst College and Williams College confused. At least one (or both?) of them is very good for both music and math, but either of them is likely to be expensive for someone who does not qualify for need based aid.