I wouldn’t be so quick to recommend some of those huge enrollment state universities to this type of super achiever. There are problems enough with the “Ivies,” the public Ivies,” Duke, and Stanford, but at those schools the super-achiever student is surrounded (for the most part) with his/her intellectual peers. Not that there aren’t achievers at those huge schools, but as a % of the student body, not so many.
Meredith is far more likely to find a large # of other students who got perfect and near perfect scores at any Ivy or “Public Ivy,” or Duke/Stanford level of competitive entry university with their selective 15K enrollments than at a state university of 45K.
I wasn’t so much recommending as commenting upon the daughter’s stated preference for a larger university. Duke is certainly 1st tier with a national reputation and a very well-known men’s basketball team. But, it’s really not that large of a school as far as total student body.