Japan offers many great options for vegetarians if you know where to look & how to order
As a long-time resident of Japan who eats a vegan diet most days, vegetarian and yes have to cave and be pescatorian at times (due to necessity of eating foods made with fish stock), it is easier than many other countries I have lived in and visited.
All shops, convenience stores and supermarkets have fresh salads, rice balls with just rice and salt or with pickled plum, cucumber or yellow daikon radish inside. Soy milk, cold noodles and a variety of breads are also readily available.
There are many eating out options in Japan too if you know where to look. There are many good recommendations of eateries all over Japan if you follow the links below.
Macrobiotic is a healthy concept created in Japan. All dishes are made without meat, fish, dairy, sugar or salt: http://en.japantourist.jp/index/search?q=macrobiotic
Vegan eateries around Japan: http://en.japantourist.jp/index/search?q=vegan
Italian Restaurants- very easy to order pasta and pizzas made vegan or vegetarian: http://en.japantourist.jp/index/search?q=Italian
Indian restaurants are a great resource for vegetarians and vegans in Japan: http://en.japantourist.jp/index/search?q=Indian