Some would say Harvard and Yale are the Oxford and Cambridge of the US. But we’re a big country, and we have a lot of schools. Many lists of top schools include these, alphabetically ordered:

Columbia University, Cornell University, Harvard University, Massachusetts Institute of Technology, Princeton University, Rice University, Stanford University, University of California, Berkeley, University of Chicago, University of Pennsylvania, Yale University

But this discussion of rankings reminds me of a quote from John Allen Paulos:

In fact, trying to convert a partial ordering into a total one is, I think, at the root of many problems. Reducing intelligence to a linear ordering—a number on an IQ scale—does violence to the complexity and incomparabilities of people’s gifts.