It's pretty hard to be a good veg in Japan, they put fish sauce in nearly everything!
Convenience stores are your best bet, they have salads and onigiri which are pretty safe. Onigiri are those triangle things covered in seaweed, filled with rice and different fillings. The convenience store at Hiroshima Station lists in English what's in each one, there's a few that are just pickled vegetables.
There's plenty of international food like Indian or Italian available which should be safe.
Before my last trip in January, I made a few little cards in Japanese that explained that I'm vegetarian and listed what I don't eat, and asks for help in finding something on the menu. Maybe you could ask a Japanese/Japanese-speaking friend to help you make something like that? Then you don't have to worry so much about explaining it to them