Japan is an island country where it is surrounded by ocean. In addition 75% of its land is mountains which could be enjoyed in various nature experiences.
Including Mount Fuji, there are many mountains all over Japan. Around in Tokyo area, there are mountains those could be climbed within a day such as Takao mountain (Hachioji) and Otake mountain (Oume).
If you are not confident enough in your physical strength to climb mountains, try hiking at a hill or a large park. Typical places around in Tokyo are Hakone, Kamakura (both in Kanagawa prefecture) and Okutama (Tokyo).
Lavender Gardens in Furano-shi, Hokkaido which normally are at their best in late July is very popular even to foreigners. Other famous fields around in Tokyo are Chichibu (Saitama prefecture) which is known for its pink carpet of moss phlox, and the autumn kokia in Hitachi Seaside Park (Ibaraki prefecture).
Visit Okinawa to enjoy the water sports which can be experienced at the sea, such as scuba diving and banana boat. If you want to enjoy in Kanto area, Izu Peninsula and the coastside of Chiba prefecture are places to be.
Many of the river in Japan is said to have steep angles considering its short length. You can experience at Tamagawa river up in Okutama in Tokyo.
Points to note
To try these nature experiences, it is recommended to find a conducting company, and make a reservation beforehand. Be sure to challenge with all equipment prepared; if it is mountain climbing, mountain shoes and rain gears, if it is rafting, helmets and swimsuits. Not to mention these experiences are seasonal, so you should check for their best seasons.