The universities in Japan are divided into three groups: (i) government-funded public, (ii) prefecture-funded public, and (iii) private. Each prefecture typically has 1 government-funded public university, 4-5 prefecture-funded public institutions, and 10 or more private ones. With few exceptions, the universities with the best academic reputation in the country are the government-sponsored public ones.
Most Prestigious. 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.
Best Engineering Schools. In no particular order: University of Tokyo, Tohoku University in Sendai, Hokaido University,
and Kyushu University. They are all government-sponsored public institutions and were
also "imperial universities" prior to 1945.
Upper-class Women's Universities. Aoyama Gakuin University, Gakushuin University, Shirayuri College, and Sacred Heart 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.
Other. Other universities worth mentioning are Seikei University and Sophia University with the latter having one of the better medical schools in the country.
Tuition Fees. As of 2006, the tuition fee for government-sponsored japanese public universities is of 560,000 yens per year for the graduate course, and of 400,000 yens per year for the undergraduate course. The tuition fees for the private universities typically oscillates between 1,000,000 to 1,500,000 yens per year, but can be as high as 2,000,000 yens per year
for the institutions famous for accomodating kids of wealthy families (such as Aoyama Gakuin and Gakushuin for instance).