Day Hikes in Japan?

On every trip I like to squeeze in at least one semi-strenuous (3-5 hour loop/~1,500 elevation gain).

I'll be visiting both Tokyo and Osaka, and from one of those cities I'd like to venture out to make a day hike somewhere.

Any recommendations? Only real requirements are fairly accessible from a major train station (don't mind taking a bus or tax from the train under 30 mins). The more beautiful, the better!

by makrman