Georgetown University
Georgetown University is an ostensibly Catholic institution located in Washington, DC, a swampy little city named for the uncle of an undistinguished King's College dropout. At least the name "Georgetown" is derived from a far more noble George.
Georgetown considers itself elite because it has some pseudo-academic degree programs in such newfangled topics as "Foreign Service", and because it graduated a president. Its claim to have trumped Columbia with the latter, though, will probably not last long.