I think you have to subdivide the Ivy League into Jr and Sr:
Sr. is Harvard, Yale, Princeton, Columbia
Jr. are Cornell and UPenn,
Brown and Dartmouth are in the middle.
I would suggest that some non-Ivy League schools have more stature than some Ivy League schools (Stamford, MIT, maybe U of Chicago), especially in certain areas. Brown, for instance doesn’t have a law school.
Your suggestion that looking closer is in order is spot on. Dartmouth doesn’t have any grad programs.
Cornell is the largest in terms of undergrads, and Cornell is a little weird in that three of its seven undergraduate colleges are state schools (Ag, Hum Ec, Industrial and Labor Relations) in which NYers are given a strong preference. The Vet school, a graduate program, is also state.