Tokyo has a good number of big high-profile art museums in its centre, particularly in Ueno and Roppongi, but thre are plenty of others to visit around the city. One that I enjoyed was Setagaya Art Museum, not far from the centre, less busy than the heavyweights but no less interesting.
It's set on the edge of spacious Kinuta Park, with paths and avenues winding past pleasant lawns and plenty of trees. The building is low and streamlined, in harmony with the surroundings, and there are several interesting sculptures dotted around outside. Walk down some steps near the entrance and you'll pass a water feature, then at the bottom there's a stone circle to admire from some outdoor tables.
Inside, the lobby has a very high semi-opaque ceiling, and a staircase round the walls leading up to the second floor. There's a feeling of light and space inside, and plenty of benches to rest on all around the museum. The exhibition rooms have plain, off-white walls so as not to distract from the art; the main rooms on the first floor have a cool beige stone floor and big, big windows allowing plenty of natural light.
They hold a wide range of exhibitions, with many different kinds of art on display. When I visited, the main exhibition was of iron sculpture by Julio Gonzalez, a friend of Picasso who also influenced his art. There was some information in English as well as the Japanese, with an introduction on the wall at the entrance, and catalogues to read around the exhibition rooms. I also saw some art from the museum's collection in the large upstairs space, though here the information was all only in Japanese: expressive line drawings by a Junsaku Koizumi, and exquisitely detailed mezzotint prints by Keisei Kobayashi, with amazingly lifelike fish, birds and insects. Past exhibitions at the museum have been very eclectic, including traditional Japanese painting, Soviet modernist posters, photography, ukiyo-e woodblock prints, ceramics, and more.
Once you've seen the exhibitions, you can visit the small but well-stocked shop which sells books, cards and stationery, and some accessories and beautiful coloured glassware. There's also an equally well-stocked art library where you can read books and periodicals, some of them in English. If you'd like to eat or drink while you're there, then SeTaBi Cafe has galettes and light meals, while Le Jardin restaurant, overlooking the park, serves classy French cuisine and wine.
Kinuta Park is about 15-20 minutes' walk from Yoga station on the Tokyu Den-En-Toshi train line, a few stops from Shibuya. The museum and SeTaBi Cafe are open from 10:00am to 6:00pm daily from Tuesday to Sunday, opening on a Monday if it is a national holiday; Le Jardin is open from 11:00am to 7:00pm (5:00pm on Sundays). Admission costs ¥200 for the exhibition from the museum collection, roughly ¥1000-¥1300 for the special exhibition.