Incidentally, sort of on a similar theme, I tend to suggest academic high flyers at “top” coastal secondary schools at least take a good look at some of the top academicky colleges in the Midwest/Great Lakes. The trick is you may have to convince them you are serious, which is easiest if you actually ARE serious. But if they buy it they may love to have you as a sort of diversity play from their perspective.
So this includes some obvious research university choices like a Chicago, Northwestern, WUSTL, Case Western, or Rochester (I consider Rochester Great Lakes even though it is in New York state). But also LACs like Carleton, Grinnell, Macalester, Oberlin, and so on.
And then there is Rice, which is obviously not in the Midwest but I think functions very similarly, and is such a fantastically desirable college (in my opinion at least) that you could very rationally prefer it to many of the Ivies and such.
And to be very clear, this is not a rankings thing (in my mind). These are colleges that for the right kid will offer great academics and a great experience, and in some cases even merit money. But they just don’t see quite as many applications from the “top” coastal secondary schools, which makes them potentially more likely than the “usual suspects” among coastal universities and colleges . . . again at least if you convince them you are really serious about considering them.