Japan has many mountain ranges. Near Tokyo, there are a lot. Included are Tanzawa, Chichibu, Okutama, Southern Alps of Japan, Mt. Fuji and Tanigawadake. All of them are one day driving distance from the city.
Sense of Geography helps you travel especially when approaching to mountain areas. Nevertheless, it's not so simple as you may think in case of this country. This is because of train connections and road conjestions. Western area of Tanzawa is very easy to get to by car; by train and buses, to get there can get cumbersome. Using the same rationale, in the reverse way, Tanigawadake is very hard to get to by car; it's expensive because of Japan's highway toll fee. By train, however, if you use Shinkansen, the travel is relatively cheap and cozy.