The quickest and easiest semi-natural area to get to from Tokyo is the Nikko area. Since access is relatively quick and easy and since the terrain is not tremendously challenging, it is often best to go to the less popular trails there if one wants to avoid crowds.
A successful day for me is when I can avoid the sight or sounds of humans. I get my fill of that every single day in Tokyo. This wasn't entirely successful as Nakimushiyama (around 1103.5 meters high) is too easy of a hike and is too close to Nikko to avoid everyone---I met a lady who looked to be in her 70s coming down the trail---but it is about the best that can be done on a one-day hike.
The real mountain is Nyohosan (2483 meters) I believe. However, as my crude map was more for entertainment than accurate navigating, I can't be positive.
