There aren't that many Mexican restaurants in Japan, especially not authentic ones. Most of them have a few things suitable for vegetarians though, such as bean burritos or vegetable fajitas. There are some Tex-Mex, American, and Fusion restaurants around which serve Mexican food.

Search this site for Recommended Mexican restaurants in Tokyo. 

Chinese restaurants might seem ok, but most have been Japanized and unless you find an authentic place where you can communicate well with the chef, they are best avoided. Generally all dishes contain seafood or meat, or at the very least, chicken stock.

There are some good vegetarian Chinese and Taiwanese restaurants in Tokyo, so search this site for recommended Chinese and Taiwanese restaurants in Tokyo.