If you visited Matsumoto castle in Matsumoto, Nagano, why not visiting Kaichi school museum too. The former school building is just 5 minutes walk from the castle.
Now it is a museum, but it was opened in 1873 and used as the elementary school till 1963. Then, it was registered as the Important cultural property of Japan in 1963. It was the first western style school building to be registered on the properties' list.
The school itself is the succesor of the oldest school not only in former Matsumoto domain, but also whole former Shinano province. Shinano province is current Nagano prefecture.
Current Kaichi elementary school moved to nearby and the history of the Matsumoto domain school.