Mt.Fuji is the highest mountain at 3776 m and definitely most famous mountain in Japan. It is second highest volcano of an island in Asia, after Mt. Kerinci in Sumatra. It is an active stratovolcano which last erupted in 1707. However, Mt.Fuji was believed that it is a dormant volcano till 90s.
Mt.Fuji is located west of Tokyo, locating between Shizuoka and Yamanashi prefectures. Both prefectures insist that Mt.Fuji is located in their prefecture and has not good relationship regarding Mt.Fuji. If you take Tokaido Shinkansen from Tokyo to Nagoya/Kyoto/Osaka, you can see the Mt.Fuji on the right side if it is clear weather. However, it is better to go to Yamanashi prefecture if you have a time to spend taking pictures.
Mt.Fuji is also possible to climb up till the summit. Many hikers climb during the night and expect the sunrise. There are many huts where you can rest and overnight at Mt.Fuji too. There are 4 routes leading to the summit and Yoshida route is the most popular but if you are Japan Rail Pass traveler, may it is better to choose Fujinomiya route. It is much less hikers than Yoshida route and also you can take Tokaido Shinkansen to Shin-Fuji station and then take the local bus. Kodama trains of Tokaido Shinkansen run each 30 minutes from Tokyo station. If you are traveling from west, Kyoto or Nagoya, definitely Fujinomiya route is the easiest way to climb Mt. Fuji.