It’s an interesting question as to whether the very best students should seek out colleges with most most comparable peer group or the best professors. It’s certainly the case that in the UK and France the choice is based on professors: if you are a potential Fields Medal winner then you want to be taught by the right professors. I don’t think Terence Tao went to UCLA for the peer group of math undergraduates. But to my point earlier, in the US the best professors are scattered around the country.
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In our opinion peer group is the most important factor, as every class is taught to the middle.
Peer group is also easier to measure than teaching quality and other intangibles, and it tends to correlate with other desirable factors.
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I think it depends on whether or not you are discussing undergraduate colleges or graduate/Phd programs. I’d lean more to peers for my kids as undergrads and more to profs post Grad programs which are smaller and often have much more interaction with profs than peers, esp Phd programs.
Yes, the best professors are scattered.
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Oft cited on this forum, but never with evidence and counter to the findings of Dale and Krueger.
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It certainly doesn’t have to be taught that way, so you aren’t offering a universal truth. The question is whether sufficiently advanced courses are available and how they are taught. While the lectures at Oxbridge are the same (and in fact everyone does the same core courses), the small group tutorials (typically groups of 2) are sorted explicitly by talent so that the best students discuss the problems in much more depth.
And different sorts of peer groups may appeal to different people. Do you want math nerds, or people with other interests?
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Lovely to hear more about your family, and kudos for sparking such an interesting discussion 
I agree with others who make the gentle suggestion that – considering the overall well-being and future of your family – MIT is almost certainly out of reach. I know you already know that Vanderbilt (and GT/FSU/etc) are a wonderful schools, with much to be excited about!!
A little personal aside: My brother recently graduated from Vandy with degrees in Electrical Engineering and Math (+ CompSci minor), and really loved his time there. He went directly to a funded PhD in computer engineering at a top university in CA and interned at Xiilinx last summer – this summer he’s deciding between Nvidia and Intel. I know your daughter has her own interests & dreams, just wanted to give an example of what success at Vandy looked like in our family.
I know it’s difficult to let go of the idea that you can give your daughter “everything” by sending her to MIT. To that I would say, look at all the other valuable gifts you can give her by saving bundle on undergrad!!
– Getting to focus on college without feeling like she should work part-time is a gift to her.
– Getting to study abroad or travel the world is a gift to her.
– Getting to choose the job/city she wants, not just the one that pays best, is a gift to her.
– Getting to see her baby brothers realize their potential is a gift to her.
– Getting to see her parents retire in their 60s/70s (and travel to spend time with potential grandkids!) is a gift to her.
All that, AND she’ll have a fulfilling and successful career to boot! My best to you & the fam 
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Excellent post! Great perspective on the many, many issues that a person confronting a decision like where to go to college (and their family) have to consider.
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I was waiting for someone to bring up Dale and Krueger.
Surprised it took so long. 
Deleted.
MIT claims to be need blind and meet all financial need.
Not having $350,000 in cash ≠ having financial need. Past a certain income/asset level, they’ll put the burden on parents to pay from current/future earnings.
Obviously this is necessary to keep people honest. Schools should also be a lot more transparent about at what typical income/asset levels FA cuts off—no reason it can’t be posted as a number the same way the numbers for full tuition/zero-EFC thresholds are posted.
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Yes, OP either didn’t apply for financial aid or was deemed not to qualify for need-based financial aid by MIT. Need-based financial aid from the other schools OP has yet to hear from is also unlikely. It seems to be missed in this discussion that OP was probably prepared to be full pay, since she couldn’t have predicted the Vanderbilt offer. There’s also the possibility that her family may qualify for need-based financial aid when the younger siblings apply for college later if she chooses to pay for this kid.
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I’m operating on the assumption, and I could certainly be wrong, that the OPs daughter chose and applied to schools on her own, and that a budget wasn’t discussed. The OP has referenced needing to “figure it out” and the fact that it will potentially impact younger siblings. Only they can clarify though.
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I think there are too many unknowns in terms of what OP knew about expected costs and ability to pay them. “Figure it out” isn’t clear as to what it means, how much of a struggle/issue it would be to pay, etc. And maybe need based aid would be possible with multiple kids in college but we do not know that. And younger siblings would need to go to “meets full need” schools but many do not. Lots of opens with a number of potential gap fillers that can change guidance/suggestions. But only OP knows further details (and some in terms of what could/will happen in the future cannot be known today).
Perhaps it doesn’t have to be that way, but that is, by and large, how it is.
Oxbridge (hardly being an example of wide academic disparity) notwithstanding.
I personally do not buy in the slightest the common argument that math and engineering are taught the same wherever you go (just go to an ABET school, and you’ll be fine, the argument goes).
And I think most of us here agree that peers’ academic level is important to some degree.
Some think that importance disappears once you are in T100. Others - T20. Yet others think that MIT/Caltech are in a class of their own. At which point does one become “elitist”?
In math class? Yes, please?!
“other interests”? 
In all seriousness, there are plenty of other interests among “math nerds”. But where it comes to core academic interests, I do want the strongest possible peer group in the narrow sense of how deep the material can be taught. My kids got enough of their time wasted in school (average graduate’s ACT score 34, to give you an idea).
And no, I do not know what the ROI is on that or how to calculate it. But I know I don’t want them to be bored in class. That is my ROI in and of itself, and I will have to trust the future to sort itself out.
Again, a disclaimer: that’s me. I am not OP.
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“Figure it out” to me is often a red flag. At least to me this is a bit scary.
One thing that we have to remember here, we are not comparing MIT with community college. We are comparing MIT with Vanderbilt. As long as a student is very smart and determined to work hard there is no academically bad choice here. Whether or not there is a financially bad choice here might depend upon what “figure it out” actually means, which most of us, including me, do not know in this particular case.
I was faced with a similar choice decades ago, but between MIT and McGill (with in-province tuition for McGill, which back then was almost nothing). I still do not know whether or not I made the right choice. I do not think that I ever could know. However, as long as you are choosing on the MIT, McGill, Vanderbilt level, I do not think that there is a bad academic choice for a strong student who wants to work hard.
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Every school has an NPC, and in our experience they are pretty accurate.
We excluded a number of less generous schools from consideration based on cost to value ratio.
I agree that “figure it out” at least can be a red flag. Could mean that there is no money there at all (or no where near enough) and its a matter of sacrificing true living expenses, savings (such as retirement), etc. Or debt. All bad things.
Could also mean some belt tightening. May mean moving some money around. Liquidating investments before they otherwise intended. Foregoing become kitchen remodeling heroes. But with all of that, no real sacrifice in true living expenses, retirement, etc.
We just don’t know. I know more than a few people who have 2-3x annual income in credit card debt. Ask them what their plan is and the response is “we will figure it out.” Other people when they say that it means money is there but some changes/choices need to be made. And everyone in between.
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Not many people don’t need to figure it out. I don’t think it means anything, other than what it says.
Many parents also have money saved and they are trying to project if the money will last for all kids or run out. Or if they are going to divide it, how will that work. In my mind, these are all aspects of figuring it out. A large scholarship can be a large factor.
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Unless you have money fully set aside for each kid’s education, you have to “figure it out”.
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