The Raumen museum (and they spell it that way, dunno why) has an extensive, not to say completely obsessive, collection of ramen-related artifacts. There are displays on the history of ramen in general, and instant ramen in particular.
But the real attraction is downstairs, in the recreation of a late-1950's neighborhood, with eight ramen shops, as well as a number of other different storefronts. The ramen shops are the real deal: eight different ramen vendors from all over Japan, each serving their own varieties of ramen. Two are from Kyushu (Hakata and Kumamoto), one from Kitakata and Sapporo each, and four from the Kanto region (Tokyo-Yokohama and environs). Each shop also offers a "mini ramen", featuring their own particular dish, so you can try lots of different kinds of ramen.
Admission is ¥300 for adults, ¥100 for children, which doesn't include the price of a bowl of ramen, which can set you back ¥1000. Still, a pretty cheap outing. There are also three and six month passes, if you want to come back a lot.
They're closed Tuesdays and holidays. Other days they open at 11AM, with last admission at 10PM.
http://www.bento.com/phgal3.html includes a much longer description than I've given here, and is the source of much of the information in this post. http://www.raumen.co.jp/home/index.html is the official site, in Japanese. (Includes Flash.)