The Sunday New York Times travel section recently ran a "36 Hours in Osaka, Japan" feature. The writer recommended as among the city's highlights the Momofuku Ando Instant Ramen Museum. It's "an entertaining pilgrimage site for noodle lovers that is named after the inventor of instant ramen — yes, that’s a statue of him outside. Mix and match flavors and ingredients to create a personalized cup of instant ramen at the My Cup Noodle Factory, or purchase one of the limited-edition varieties from a vending machine in the tasting room."
I've never been to the Osaka museum, but I've visited the Shin-Yokohama Raumen Museum twice. ("Rauman" is the way the museum spells it.) It's only about half an hour from downtown Tokyo by train, and an easy walk from the Shin-Yokohama station. It features a large hall that recreates the Tokyo of 1958, the year instant ramen noodles were invented. Surrounding this two-story hall are branches of famous noodle restaurants from around Japan, each featuring a local specialty.