Your typical Japanese meal consists of a protein source (fish, shellfish, chicken, beef), a bowl of soup, some vegetable side dishes (pickled or not), maybe a side of sashimi, and a bowl of rice or noodles. Many restaurants serve either sashimi (raw fish) or grilled fish as a main dish.

Just avoid the rice or noodles.

Miso soup is made of fish broth, soybean paste, and usually green onions and tofu, although other variations are possible, such as miniature shellfish. It's almost always served as a side dish, though, not as a meal.

If you must eat at a noodle shop, soba (the grayish noodles) is made of buckwheat and has a lower glycemic index than udon (the white wheat noodles).

Okonomiyaki has some flour in it, but it's mostly a giant omelet filled with your choice of meat or seafood, topped with mayonnaise.

The chicken version of shabu-shabu is called mizutaki.

Shoga-yaki is pork stir-fried with cabbage, green onions, and ginger.

The Chinese-style restaurants (chuka ryori) feature all kinds of meat plus veggie stir-fries.

Unless you order a fried rice (chahan) dish or a donburi (rice with stuff on top), rice is served on the side.

These days, every imaginable type of ethnic cuisine is also represented in Tokyo, so you can try those restaurants as well.

In most cases, affordable restaurants in Japan have either plastic models of their fare or photographic menus, so you can tell by looking whether a given offering is within your restrictions.