If you follow any Japanese culture site like Kotaku East, you're going to find out about a lot of really specific and very cool looking museums and theme parks. They're laser-focused as a rule and really cool looking.
The Totoro House is the best I've stumbled across so far. It's a life-size recreation of Hidaka and Sakamoto's house from My Neighbor Totoro. Everything is there, from the stacks of books in the library to the sandals placed underneath the porch.
It's a nostalgia trip to look through the tourist photos you can find online. Kotaku East has a huge gallery that just made me smile. The incredible level of detail will take your breath away.
The bizarre factor comes in with a simple realization: there's already a gorgeous Studio Ghibli-themed museum and the Totoro House is not part of it. This is a stand alone attraction in a separate park. Hidaka and Sakamoto's home is removed from tributes to Castle in the Sky, Porco Rosso, and even the Catbus from My Neighbor Totoro. The existence of the Totoro House is a testament to the popularity of Miyazaki in Japan and the staying power of a very sweet story about young girls discovering a fantasy world hidden in and around their new home.
The Ghibli Museum has a huge Totoro display in the permanent exhibits. All the major characters are there for photos and interaction (though children are the only ones allowed on the Catbus). It's also a contained building with rotating exhibits and probably did not have the space available to dedicate to a recreation like the Totoro House.
The official site for the Totoro House is in Japanese and does not have a clean English translation outside of automated browser services. You get the gist of it from the descriptions. The house's appearance changes with the seasons because of the landscaping and the interior decor. It's an impressive undertaking sure to make any animation fan smile.
You can find more Bizarre, but True stories at Sketchy Details.