Japan is not a really easy country for vegetarian people because fish, and specially meat, consumed in tiny amounts, but they are everywhere. I would say that sometimes meat is used more as a condiment than as an ingredient. Also, in my experience, most of Japanese don't consider that things like the bonito flakes they put in the stock are "actual meat", and when you say that you don't eat meat, they actually understand that you don't eat steaks or sashimi.

Said that, there's a nice vegetarian Ramen shop in Tokyo Station:

http://ts-restaurant.jp/tantan/