Dedicated to the work of animator Hayao Miyazaki and Studio Ghibli, the museum is a 15-minute train ride from both Shinjuku and Shibuya. Even if you've never heard of Studio Ghibli before it's worth a visit, and the nearby neighbourhood of Kichijoji has a slightly bohemian feel that is unusual to come by in Tokyo.
Ghibli Museum, 1-1-83 Shimorenjaku, Mitaka-shi, Tokyo 181-0013.
www.ghibli-museum.jp
The nearest station is Mitaka (Chuo Line), but I would recommend walking there from Kichijoji station (Chuo and Inokashira Lines).
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