Hayao Miyazaki's animation studio has a very cool museum in Inokashira Park, in Mitaka, a suburb west of Tokyo. It's great for kids. There's a giant cat bus to play in, with piles of big black poof balls with eyes to throw around (modeled after those little creatures in My Neighbor Totoro, made of soot I think); a trippy zoetrope with 3D models of the Totoro characters, spinning around on a circular platform (a strobe LED makes it look like they're in motion -- there's Mei jumping rope!); loads of watercolor sketches and a few cels from Totoro and other Miyazaki movies; film reels you can manipulate yourself; a theater showing an animated short (in Japanese) about a lost dog (the film changes every few months I think); and a gallery showcasing other animators' work (right now it's the 1954 British animated feature version of Animal Farm, which is actually being re-released here, we're told, and will soon be showing in a couple theaters in Shibuya).
The robot from Castle in the Sky lives up on the roof. We paid him a visit last Saturday.
[Thanks, Stace, for telling us about this place all those many months ago. It just took us a while to get there!]