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.
Mount Ibuki, located in Maibara near Lake Biwa is one of Japan's 100 famous mountains. It has great views over the surrounding mountains and lake. Unfortunately the summit has undergone a lot of development and is more akin to a shopping centre. There is a road that leads to the summit and it isn't rare to find women knocking about in high heels and fashion not suitable for climbing mountains.
There are also lots of abandoned buildings on the mountain such as omiyage gift shops and a gondola station which housed the old ski lift. If you are adventurous you can explore the abandoned buildings.
One of the most underated parts of the Japanese alps. The central alps is unbelieviably beautiful, if someone blindfolded you and told you were somewhere in Europe, it would be entirely believable. The hike is very straight forward, it can be combined with a multiday hike and other nearby peaks such as Houkendake.
The tallest peak on the Kyushu mainland standing at 1,791m. Stunning active volcanoes and vibrant colours. Lots of different peaks to do along the way and always changing scenery.
The hike offers an alternative to the rope way which takes you to the top of Mt. Misen, the highest peak on Miyajima Island. At the top of the mountain there is a good viewing platform from which you can see the Seto Inland Sea and the main land of Japan. The track is far less crowded than the ropeway and gives opportunity to see some of the more wild deer which are less used to human interaction.
Mt. Myogi offers a thrilling hike with long sections of scrambling. It is not for the faint hearted but the views are spectacular. Although not one of the 100 famous mountains, it honestly should be as its shape is iconic and offers a hiking experience unlike any other.
A pretty decent look at some karst topography, not as cool as Mt. Nuki in Kitakyushu but does the job. Akiyoshidai is much more expansive and this hike can be combined with many others to make for a full day.
Mt. Nokoyama is located deep in the sticks of Gifu Prefecture. It has a 360 view over the surrounding river, farmlands and mountains. Not particularly hard, makes for a good day trip.
Norikura is one of Japan's 100 famous mountains and one of the 20 odd mountains in Japan that are over 3000 metres. On a clear day you get jaw dropping views of the Hotaka Mountain range and the northern alps, if you are lucky you can see as far as Fuji. There are volcanic lakes galore. It's worth the trek out to Norikura.