Daughter has great choices. Not sure what type of engineering. Leaning toward cornell but not sure.
CMU, Cornell and Michigan are the best overall choices, assuming cost of attendance is not a concern. UIUC is just as good in Engineering, but not as strong overall, should she change majors, and UVa is as good overall, but not as strong in Engineering.
Is she is leaning toward Cornell, then she should go. It is the best Ivy League in Engineering, and truly an exceptional institution.