[samurai007]

I think if you go toward the end of May, Kamikochi should be ok to hike. I went not much later, in June, and the only snow was high in the mountains, far away from the hiking area which is in a valley between the mountains. But ask around while you're in Takayama.

You can hike to the top of the mountain on Miyajima Island, off the coast of Hiroshima. That only takes a few hours going up, but it's a pretty steep climb. You can also hike up the pilgrimage trail to Koyasan instead of taking the gondola up, if you are going there.