Sanageyama - literally monkey throwing mountain, is a nice short hike with good views over rural Aichi located in Toyota city. A good escape from Nagoya and some cool waterfalls.
Out in sleepy Akechi is Mount Suwagane. Only do this mountian if you are bored and you literally have nothing better to do. Views are limited and the path is diliapidated.
Mount Yakedake is an active volcano in the northern alps in Japan. It is one of Japan's 100 famous mountains and provides fantastic views over the surrounding area.
Mt. Zao is one of Japan's 100 famous mountains, located in Yamagata Prefecture part of the Mt. Zao quasi-national park. Mt Zao is an active volcano that is also famous for being a ski resort in the winter with the natural snow monster phenomenon.
Mount Fuji is the tallest mountain in Japan and possibly one of the most iconic peaks on Earth. Although the views from Mt. Fuji are nothing particularly special compared to other mountains in Japan, the sunrise from the top is biblical and is more than worth the trek to the top.
Mt. Omuro is a designated national monument by the Japanese government and is part of the Fuji-Hakone-Izu National Park. It's a very green extinct volcano
One of the 100 famous mountains in Japan, Mt. Aso is truly epic. Being one of Japan's most active volcanoes, it is to be feared as it constantly plumes sulfuric gas that can be deadly. But thanks to its volcanic activity, Mt. Aso has scenery unlike anywhere else in Japan except maybe Mt. Kuju. Filled with lushious green fields, black volcanic deserts and boiling lakes. Mt. Aso is worth the trip.
Some would describe this hike as A.S.O too much volcano or even danger volcano.
Mt. Chausuyama is the tallest mountain in Aichi prefecture, part of a Quasi-national park. It is very easy and can be smashed out with the neighbouring mountain in probably less than two hours. There are some good mountain biking opportunities if you are of that persuasion, maybe good for trail running as well. In winter, the mountain becomes a ski field.
Futatsumoriyama is out in the sticks of Gifu Prefecture. Summit has 360 views of the surrounding mountains. It's not the best nor the worst mountain.
Houraiji is an ancient temple that was founded somewhere around 700 AD. It was secluded in the mountains and became a place for serious aesetics to learn about esoteric Buddhism. Because of its heritage of being an important Buddist temple, the surrounding forest was not destroyed in the great purge of forests conducted by the Japanese government. It is a rare example of ancient trees. It is very biodiverse which is a great change from the usual monoculture of trees you find on Japanese mountains.