At the Ghibli Museum, we ate at the Straw Hat Cafe (which reminded me far too much of One Piece). It was pretty and brightly colored! Also, the food was delicious.
Bonus picture! This was my order...(delicious) strawberry cake and a drink which, so far as I can remember, was called "Looking Up Into a Clear Blue Sky Cream Soda." I didn't even really want cream soda (which in Japan, by the way, actually means soda with ice cream) - I just got it for the name. It was totally worth it.