Mount Minobu (身延山) is a pleasant hike located in the town of Minobu in southern Yamanashi. It is famous for the temple Kuon-ji (久遠寺), the main temple of the Nichiren sect of Buddhism.
From the large wooden gate, you can hike up the Stairs of Enlightenment (or cheat and take the road up) to reach the temple area. From there, you can continue to hike to the summit (about a 2.5 hour hike) to reach another section of the temple. Alternatively, there is a lift that will take you up to and down from the summit of the mountain for a small fee.