Sit by a clear river and let the day drift
The Kakita, the Nagara and the Shimanto are often called Japan's three great clear rivers. Spend an unhurried day on a riverside path or a low bridge, just watching the water go by. They are far apart, near Mount Fuji, in Gifu and on the island of Shikoku, so pick one.
A short river, only about 1.2 km long, that rises from springs fed by snowmelt from Mount Fuji, pouring out about 1.1 million cubic meters of water a day. From the park's two observation decks you look down into clear pools where the springs push up through the sand. Entry is free, and it is a short taxi ride from Mishima Station on the Tokaido Shinkansen.
A river in Gifu that flows 166 km with no dam on its main stream except a weir near the sea. From May to mid-October you can watch ukai, or cormorant fishing, from a sightseeing boat in Gifu City: at night, fishermen guide trained birds that dive for sweetfish by the light of a fire hanging from the boat. Gifu is about 20 minutes by train from Nagoya.
A chinkabashi, or sinking bridge, built low and without railings so that in a flood the water and floating logs pass over it instead of tearing it away. It crosses the Shimanto, a 196 km river in Kochi often called Japan's last clear stream, and you walk across just above the water. It is a long way from the big cities, so plan it as part of a trip to Shikoku.