The vegan lifestyle is new in Japan; vegetarianism is not. Shojin ryori (精進料理) - the vegetarian diet of the Buddhist monks - has been around for centuries in Japan. Japanese cuisine (and markets) are conducive to vegan cooking. (Lots of lovely veggies.) If you are used to fancy vegan fare and need a kitchen, consider renting an apartment. If a microwave will do the trick, you can probably rent one. Budget travelers staying at the nationwide Toyoko Inns will generally find a microwave in the lobby area.