I've had a few people ask me about food, because they don't like seafood or sushi. After my initial "what the hell is wrong with you" reaction...it's not raw fish, all the time. But fish is a mainstay of the Japanese diet, and you'll have to work pretty hard to avoid it completely. Vegan and gluten-free folks will have a more difficult time, although I did see a few menus mentioning those two restrictions. I have to say though - I never saw anyone who seemed to be requesting any dietary accommodations. I think this is a uniquely American, certainly first-world, demand.
And unless you know Japanese, I'm not sure how you would even make the request. We had a hard enough time figuring out what, exactly, we were eating sometimes. While ALL of the restaurants had picture menus (this is a thing in Japan, and not just in tourist areas - menus with pictures, and cases displaying the various dinner options), the English translations were...interesting. I was never sure that "offal" really meant what I thought it did. And were "tendons" really tendons, or did they mean tenders? Other than pickled vegetables - also a thing in Japan, and not my favorite - and some of the jellied sweets (again, not a favorite), we never had anything that we didn't like. It was all good, filling, and beautifully presented, even in the tiny diners and bars.
Noodles are common (udon, soba, ramen), rice of course, tempura and other breaded fried preparations. "Hot Pot" is a soup or stew, usually cooked by you, with ingredients brought to your table. In addition to fish and seafood, you will always find chicken and pork, and usually beef. Other foods are also easy to find - and as Vonn pointed out, we don't eat one type of food at home every day, ever, and neither do the Japanese. Italian and French cafes are easy to find; Chinese, Thai and Indian; and of course, McDonalds, Starbucks and other international chains can be found. Even Denny's.
About the sushi. We did have mediocre sushi once, at a chain called Sen Zushi in Tokyo. Otherwise, it was all excellent, even at the conveyor-belt sushi place. And "sushi" in Japan is a slice of raw or seared fish on a rice ball. A "roll" is a different category here, called "rolls" (duh) and the list is often very small, unlike in the States.
Green tea. I hate green tea. And "tea" is almost always...green tea. To compound the issue, they have green tea flavored everything. Sweets, ice cream, Kit Kats, you name it. I don't get it.