I do not know which schools are Tier One, Tier Two & Tier Three without more criteria. But, for prestige purposes, my totally subjective impression is :
That among the top group of most prestigious US colleges & universities are:
Harvard, Yale, Princeton, Stanford, MIT, Penn-Wharton School, Caltech, Juilliard, Curtis School of Music, US Military Academy at West Point, US Naval Academy-Annapolis, US Air Force Academy-Colorado Springs. ( Also, "an Ivy–as in: “I went to an Ivy League school for undergrad.”)
The next tier:
Columbia University, Univ. of Chicago, Northwestern University, Duke, Penn, Johns Hopkins, UCal-Berkeley, Cornell, Dartmouth College, Brown, Williams College, Amherst College, Wellesley College, Swarthmore College, Pomona College. (Also Georgetown School of Foreign Service & Univ. of Michigan-Ross School of Business.)
And, finally, the “this will make me enemies” next tier:
University of Michigan, Rice University, Vanderbilt University, University of Notre Dame, WashUStL, Georgetown, UCLA, Bowdoin College, NYU- Stern, NYU- Tisch, NYU (philosophy), Georgia Tech & Carnegie Mellon University.