Afuri is known by many to be the best ramen chain in Japan.  Its cheap and the broth is cooked over the entire day. Soft, medium, or hard noodles can be ordered. Of course the foreigners are the only ones to order soft. They also have super spicy ramen which I like.

http://www.yelp.com/biz/%E9%98%BF%E5%A4%AB%E5%88%A9-%E6%B8%AF%E5%8C%BA-3