Being a vegetarian/vegan in Japan can be quite tricky since Japanese cuisine relies heavily on broth made from meat or seafood. The different vegetarianisms are not widely known in Japan, so it probably is the easiest to explain to people that you are “a vegetarian who does not eat ________” instead of saying vegan, ovo-vegetarian, lacto-vegetarian, pescatarian, etc.
A wide range of vegetables, legumes and soy products are readily available in restaurants and in grocery stores in Japan. Seasonal vegetables and fruits are often priced quite reasonably (foods that are not in season are a lot pricier so get to know the agricultural calendar of Japan!). In Mie, there are a number of restaurants that offer vegetarian or vegan options so they are worth scoping out for.
*Japanese sweets widely use a plant-base jelly called agar, or 寒天(kanten) so look out for these when you feel like having a refreshing, cool treat in the summer!