One of the reasons we ventured outside of Tokyo on our recent Japan trip was to see a few recently built museums (I was traveling with some architects). 

The first one was the great 21st Century Museum of Contemporary Art in Kanazawa. If you’re familiar with the work of design studio Sanaa, you’ll understand it when I say that the space is quite minimal. Still, it works very nicely, also because they had a few art works commissioned as part of the architecture. There’s one of those James Turrell sky-windows, but the real clincher was this clever, but beautiful piece by Argentinian artist Leandro Erlich. 

They also had a really nice collection, mixing Western conceptual chaps like Jan Fabre and Damien Hirst with local artists and incorporating more ‘popular’ platforms like animation and figurines. I particularly liked this great installation by Yoshitomo Nara, in collaboration with graf.

The other museum we visited was possibly one of the most amazing buildings I’ve ever seen. The ChiChu museum was commissioned by some big cheese at the Benesse Corporation, on the old fishing island of Naoshima, just to house his 4 ‘Water Lilies’ by Monet. That’s right: one museum for 4 paintings. But it’s an amazing space, designed by boxer-turned-architect Tadao Ando and built more or less into a hill. 
It’s all very Nihon-clinical and almost lab-like (you have to take off your shoes before you tread on the white marble mosaic that makes up the floor of the main room), but it’s so well done it makes you smile. 
Taking pictures if forbidden, but this person managed to take a few.
Just go.