When you get off the train at Minobu, you will find yourself in the quaint, quiet downtown strip of the mountain town. Very much like something out of the past. Fall is particularly nice, when everything is wrapped in fog and the leaves are blazing red and yellow. Have yourself some ramen or udon with mountain vegetables and catch the bus to Mt. Minobu (about 15 minutes away).
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The local high school's baseball team uses it to train.
(There's also an easier trek through the forest for those who can't make it.)
There's also a parking lot for cars in case you're driving. If you're interested, you can also take a cable car further up for a view of the mountains all around.