It's very difficult to be a vegetarian in Japan unless you do all your own cooking. Even then, if you do not know Japanese, it is difficult to check the labels to make sure everything you are buying is completely vegetarian.
Eating in restaurants is very difficult as the Japanese LOVE to sneak meat in almost everything. Even if it looks like it doesn't have meat in it and the menu makes no mention of meat, you might be surprised when you look closer. There are probably tiny bits of pork stuffed in it. If you tell your servers that you don't eat meat, they'll usually try to accomodate you, but the Japanese idea of vegetarian is
probably different from yours. Vegetarian might just mean that you usually don't eat meat (but sometimes is ok), or that anything that doesn't contain giant hunks of meat is ok (such as ramen broth that is pretty much liquid pork).
As far as new vegetarian Japanese food, if you're feeling really brave, try some
konnyaku. It's a little bit terrifying in texture, but the taste is very unoffensive.