Just remembered now, in Kyoto you can hike up the hill behind Fushimi Inari Taisha. This is the famous shrine with thousands of orange torii or gates. It's a proper hike, and quite steep at times. I remember it took a lot longer than I thought it would, because the map they have on location is not really drawn to scale. Also getting there is very simple, just hop on the JR Nara line from Kyoto Station. Unlike some of the other shrines in Kyoto where you have to wait around for the bus.

http://www.japan-guide.com/e/e3915.html