There are two international airports around Tokyo, Narita (IATA: NRT) and Haneda (IATA: HND). Haneda is closer to the city, but Narita is served by more air lines.
Tokyo Monorail is the usual option. Take this until Hamamatsucho stop, where you can transfer to the Japan Rail lines. Major stations like Tokyo, Shibuya, Shinjuku, Ikebukuro are accessible on the JR Yamanote line.
There are several different options to get to the downtown from Narita airport.
Ochanomizu University is in the north western part of the downtown, close to Ikebukuro. Be carefull, it's not in the Ochanomizu district (where Ochanomizu and Shin-Ochanomizu stations are)!
The closest Metro stations to the campus are Myogadani station (M23) on the Marunouchi line and Gokokuji station (Y11) on the Yurakucho line. Both lines are connected to Ikebukuro station.
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My office is located at the 6th floor (top floor) of Science Building 1. The room number is 642, close to where it's connected to Science Building 3. The campus map is here (Science-1 is marked #18).
The math department of the University of Tokyo is outside of the Yamanote line, close to Shibuya. Take the Yamanote line (inner loop) to Shibuya station, then change to the Keio Inokashira line, and go until Komaba-Todaimae station. The campus map is here (to the right). See also Yasu's guide.
The usual way is to take the Shinkansen express train operated by Central Japan Railway (JR Tokai), either from JR Tokyo station or Shinagawa station. From Ikebukuro, these stations are reachable by the Yamanote line (outer loop, to Tokyo station). During most of the day the trains depart every 10 minutes, but make sure to take the Nozomi train (Hikari and Kodama also stop at Kyoto, but they go slower stopping at many other smaller stations on the way). Shinkansen train to Kyoto takes two and a half hours, and costs about 14,000 JPY. It takes about one hour from the station to Kyoto University, on bus line 17 (Kyodai Nogakubu-mae or Kitashirakawa). Their campus map is here.