The Museum of Art in Onomichi, Hiroshima, is located on top of the mountain overlooking the town and the nearby islands.
It was designed by world-famous Japanese architect Tadao Ando, and while the combination of modern glass and steel with the traditional curved roof is interesting, it is in my opinion not one of his better designs.
The museum hosts various changing exhibitions and has a cafe with great views.
It is possible to drive up, but the easiest way is to take the Senkoji Ropeway. The museum is a few minbutes walk from the mountaintop station.
It's open from 9 to 5 and is closed on Mondays.