" I just know that my DD and I tend to be polymaths, and that we often feel a bit insecure in groups of pointy types, since we don't seem to have a "one thing" the way that they do."

Interesting comment... my D says she picked Harvey Mudd to attend because she felt it was the college that would feed her polymath tendencies more than any other. Note it was NOT the Ivies she felt this way about. Too many parents and students are asking the wrong question ("How do I get my kid into an Ivy?"). The right question is, what schools will allow me to achieve my goals and be a good fit for me?