Mt. Daibosatsu (大菩薩岳) offers a moderate hike (about 1.5 hours up) with a view of Mt. Fuji. The mountain, located in Koshu, Yamanashi Prefecture, is one of Japan's "100 best mountains," and is 2,057m tall.
I was lucky enough to go on a day where it was clear enough to see Fuji. As we hiked farther up, the view got better and better. Going down is a bit rocky, but we completed it in tennis shoes. The next day your legs will be sore, but don't forget to enjoy the onsen (hot spring bath) and famous Yamanashi wine afterward!