
Give one of these a whole day.
Japan spent thirty years building art museums in unlikely places, and the result is that several of the best are on islands or in the mountains rather than in cities, and the building and the site are as much the point as the collection.
Naoshima and the islands around it in the inland sea are the extreme case: museums cut into hillsides, old houses converted into single works, and a large spotted pumpkin on a pier. It is a full day by ferry and it does not feel like museum-going.
Island and rural museums close on set days, often Monday or Tuesday, and some require timed tickets. Check the day before you sail or drive — there is no second attempt on a day trip.
Check the closing day, and whether tickets are timed. This is the single most common way a good day here goes wrong.
Photography is often not allowed inside these buildings, including some of the famous rooms. The signs are clear; the rule is enforced politely and absolutely.
Each links to its prefecture.

Museums in hillsides and houses converted into single works. A full day by ferry.

A garden looked at through windows, seen only through the windows, with the paintings inside.

The illuminated festival floats, kept and lit all year by the station.

Sculpture on a mountainside, with a hot-spring foot bath at the end of it.

A circular glass building in the middle of Kanazawa, next to the great garden.

Everything from national collections to a museum of one artist. Many close Mondays.