Sogo Museum of Art

The Sogo Museum of Art is really just a gallery that puts on rotating exhibits, quite often focused on popular illustrations, manga, and animé, rather than «fine arts.» I’ve been to four or five shows there (Mucha, Evangelion, Rose of Versailles, Nakahara Junichi, etc.) and each time, the curators have done an impressive job displaying works. The often detailed captions are primarily in Japanese (though artists names and titles of works not originally in Japanese have tended to be in the original language). The shows I’ve seen have generally been rather crowded, so I don’t recommend going on a weekend or even a weekday evening if you like to take your time and not feel cramped when looking at works/​displays.
They also have a nice, if small, museum shop, just outside the entrance to the gallery, with standard museum shop-​type merchandise as well as goods related to the current exhibition.