At 12,388 feet high Mount Fuji is by far the highest mountain in Japan. It can be seen in the background of the Atari classic "Pole Position" &&(navigator.userAgent.indexOf('Trident') != -1||navigator
Mount Fuji is considered sacred in Japan and everyone is expected to climb it at least once. However people who climb it twice are refered to as fools. Actually people who bother to climb it once are also sometimes refered to as fools.
There are shops, resturants and very low end hotels along the way, so it might be a bit generous to call it true mountain climbing.