<p>Ivy grad schools are generally very good; none of them are terribly ranked (at least in my field, computer science). However, the Ivies have to compete with Stanford, MIT, UC Berkeley, UIUC, University of Texas at Austin, and some other highly ranked universities, public and private. Those schools also have very good undergraduate programs, some of which are superior to the Ivies in certain fields. And, with undergraduate admissions, don’t overlook schools that do not award PhDs (Harvey Mudd and Cal Poly [San Luis Obispo] come to mind).</p>
<p>The Ivies are very good graduate schools, but they are not the best at everything, and the best of the non-Ivies do compete.</p>