Day hikes from Tokyo, Kyoto, Osaka

Hi
I'll be spending 2 weeks in Tokyo, Kyoto and Osaka in July. I'm wondering if there's any day hikes you could suggest that aren't based on city views. I would describe my hiking level as intermediate.
Thanks in advance

Mt. Myogi in Gunma prefecture from Tokyo: http://www.japan-guide.com/community/scarreddragon/report-1589

Easy day trip with different hiking trails to fit your level. Also in the Gunma area are trails around Mt. Haruna and Mt. Akagi. (And I just realized how ugly the pictures in that report are... sorry about that, it's much nicer in person!)

Kamakura area also has some great trails leading from some of the shrines in the Kita-Kamakura area through a park and mountain to the Daibutsu great Buddha in Kamakura proper. Although its a pretty easy trail that takes an hour and a half or so, it's got nice greenery and views of the ocean.

Definitely check out this page: http://www.japan-guide.com/e/e2427.html

And although I'm not sure if you could do it in a day trip, this hike looks pretty awesome too: http://www.japan-guide.com/tour/2015/e/north/day16.html

Many... Click... http://www.japan-guide.com/e/e2427.html

Lonely Planet has a whole book about hikes in Japan (including several day hikes) - check that out for ideas!