Hiking is very popular in Japan. Especially day hike is popular among elder Japanese throughout the nation. If you want to enjoy the nature of Japan, I recommend to go for a hiking.
The most popular place for hiking in Greater Tokyo is Mt.Takao in Hachioji city. Thousands of hiker visit each day and the number will increase during autumn. To reach Mt. Takao, take JR Chuo line to Takao and change to Keio line to Takao-sanguchi station. Cable car and chairlift are available. After the hiking, you can visit a nice confectionery store in Hachioji, Tea Cozy.
If you are in Kansai area, Osaka, Kyoto and Kobe, I recommend Mt.Rokko in Kobe or Mt. Hiei in Kyoto/Otsu. Especially Mt.Hiei is nice due to you can visit one of the famous temple in Japan, Enryakuji temple. There are two ways to reach Mt. Hiei. Visit from Shiga prefecture, Otsu city or from Kyoto. I recommend to visit from Otsu and then go down to Kyoto. In this case, take JR Kosei line to Hieizan-Sakamoto station and walk or take a bus to the cable car station.