Tokyo is home to Japan's top-6-university club: (i) University of Tokyo, (ii) Waseda University,
(iii) Keio University, (iv) Housei University, (v) Meiji University, (vi) Rikkyou University. A parallel can be made between the latter universities and the ivy league: i.e., they are the most famous institutions in the country and are considered a special club with many baseball/soccer games and other cultural events organized between themselves. Of those, only the University of Tokyo is a government-sponsored public university while the
others are private.
Aoyama Gakuin University, Gakushuin University, Shirayuri College, and Seikei University are four other private Tokyo universities which, while not ranked highly academically, are nonetheless famous for consisting mostly of female students from a wealthy milieu. Another university worth mentioning is Sophia University which used to be
a women-only institution, and now has one of the best medical schools in the country.
More information on japanese universities.