Located 1200 meters above sea level in Gunma Prefecture is a hot spring known better than the rest: Kusatsu Onsen. There are 13 public baths at Kusatsu, some of which are free for tourists and townsfolk alike. And it just so happens that it’s under 3 hours by train from Tokyo.
This onsen had already been famous for centuries, but only became the most famous somewhat recently, when a German doctor teaching at Tokyo University declared the water to have unique health benefits. The water comes from nearby Mount Kusatsu-Shirane, and has different degrees of clarity and cloudiness in different baths. The locals themselves claim it can cure all ailments but lovesickness. I suppose you’ve got to try it to find out.