You can check out their website (English) for a list: http://www.raumen.co.jp/english/#manual
When we went, the entrance fee to the museum was 310Yen. Basically the museum's interior looks like Japan in the Showa period. It is not so much a museum though, but more a place to eat.
Several famous Ramen shops from all over the country are present. The shops frequently change, but they always have vegan options.
We had veggie Ramen at "Narumi Ippudo" and at "Komurasaki". Narumi Ippudo's ramen had a very light broth. At Komurasaki we took a "Compare veggie with non-veggie set" for 1,240Yen with a bowl of both versions. If you have someone eating meat with you, this is definitely recommendable. Then there was "Muku Zweite" a shop that originated in Germany and came to Japan later. The veggie Ramen are miso based and really good.
|Ramen Museum from inside|
|Narumi Ippudo Vegetarian Ramen|
|Komurasaki Ramen: Veggy and Non-Veggy|
|Muku Zweite Vegetarian Miso Ramen with extra egg|
Shin-Yokohama Ramen Museum
2 Chome-14-21 Shinyokohama
Kohoku Ward, Yokohama, Kanagawa Prefecture 222-0033