Everyone else gets to decide which universities are the best, why not you? This list includes schools usually considered "national research universities" by the Carnegie Foundation. There are a few schools (Villanova, SUNY Geneseo, Butler, etc) that are considered Masters Universities, but are institutions with academic recognition on a national level.
http://www.ranker.com/list/best-major-universities-private-and-public-combined-your-votes/mixmaster-reid, anything, other,
Brown University
Carnegie Mellon University
Columbia University
Johns Hopkins University
Northwestern University
Princeton University
Rice University
University of California, Berkeley
University of Chicago
Yale University