I joined a meetup in August and hiked the Nishizawa valley (西沢渓谷 - Nishizawa Keikoku) which is famous for its 7 waterfalls. You can find some Japanese leaflets scanned here and here.
We met at 8:15 AM at Enzan station (JR中央本線 塩山駅) and took a bus (山梨交通) towards the bus stop 西沢渓谷入口バス停 from where we started the hike. You can see my GPS log on Google Earth for a detailed description of the route. If you want to take your own I suggest using the "Easy GPS logger" application on your smartphone. It produces a .gpx file that you can read from Google Earth.
The hike was really pleasant. Most of the route goes through a forest along a river with wonderful waterfalls. Definitely a nice mountain to try in Summer.
You'll also have the chance to cross a hanging bridge. Nothing to be scared of!. After the hike, we went to a Japanese hot spring (onsen) for a relaxing bath. Finally, I had some grapes from this region (Yamanashi prefecture) and went back home by train.