I'm mostly staying out of this thread because it's pretty US-specific (thank goodness!) but as an academic I will say one thing: when considering perceived university rankings, it really matters what your child will be doing with the degree, because universities are not homogeneous: good departments can exist inside not-so-good universities and vice versa. So do you pick good department or good university? One approach would be: if your child expects not to use the specific education in the department (the major to you I guess) then pick good university, for impressing people later. If s/he does expect to use it (e.g. to go on to graduate school) then pick the good department, because people in the business know the departments and couldn't care less about the university overall. Most people should care a lot more about the quality of the department than they apparently do.

YES. A thousand times yes.

This is what drives me nuts about the US ranking systems. They generally seem to pretend that those differences don't really matter, or only matter in a few fields that are obviously radically set apart from mainstream liberal arts curriculum-- like fine/performing arts, or engineering.

Otherwise, they make no distinctions. So if Princeton is #3, what does that mean? Does it mean that it has the #3 theoretical mathematics program? The #3 creative writing program? Anthropology? Of course not.

It's stunningly difficult to ferret that information out and mostly, it becomes most efficient to do so by parsing which graduate programs have the highest ratings in particular disciplines-- because THAT is relatively easy to discover based upon publication rate and rankings, grantsmanship, graduate placement, etc.

One reason why dealing with a polymath is so frustrating in this climate is that a great many lower-tier schools do have just one or maybe two (often related, like math-physics or anthro-archeology) excellent programs, but the rest of the campus is rather lackluster. Finding a place which is a good match for a child who has three or four serious interests as potential majors is a bit of a challenge.
Schrödinger's cat walks into a bar. And doesn't.