Day hikes from Tokyo, Kyoto, Osaka

Hi!
I'll be spending 2 weeks in Tokyo, Kyoto and Osaka in the July period (summer). I'm wondering if you guys could suggest any day hikes around those 3 areas. I'm looking for more nature scenery hikes, rather than city views.

Thanks in advance.

You might try the Kumano region south of Osaka. If you time your trip right, you might be able to also catch the Nachi Fire Festival. Here are some links:

http://www.japan-guide.com/e/e4952.html
http://www.japan-guide.com/e/e4955.html
http://event-carnival.com/japan/nachi-no-hi-matsuri-festival

I hope this helps.

Kamakura, a side trip from Tokyo, has a couple of trials. A nice one that also has some temples and shrines along the way is the diabutsu trail.
http://www.japan-guide.com/e/e3113.html
Mt. Fuji.

From Kyoto - Fushimi Inari is a nice mountain climb. While it starts off crowded it thins out the higher you get. And Miyajima island has a mountain to climb.

How about Mitakesan? much cooler than in Tokyo 　
http://www.japan-guide.com/e/e3036.html