The Yamanashi Prefectural Art Museum has a nice mix of domestic and international art inside, but without even paying a yen you can spend a lovely morning strolling around the sculpture garden, Geijutsunomori Park. Bring a picnic, play on the art objects, and marvel at the visage of Mt. Fuji in the near distance. Kid friendly, there are lots of benches and expanses of green grass to run around or spread out.
Curious person loves coffee shops, walking, vegetarian food, thunderstorms, and puttering.