The Shin-Yokohama Rāmen Museum absolutely cannot be missed. It's a rotating series of ramen restaurants all together under one roof to celebrate the history of ramen, and the building is spectacular. It's decorated in what is my all-time favourite style: buildings made up to look like you're outside during the night-time, when you're really inside during the day-time. The restaurant area is made to look like a Tokyo neighbourhood circa the late 1950s, in honour of the invention of instant ramen.
It's delicious _and_ whimsical — what more could we hope for?
Here's a photo from a visit a few years back: