You should try some traditional Edo-style food. Edo is the old name of the city Tokyo.
Traditional Edo-style food are for example: Dojo-nabe (loaches hotpot), monjayaki, Negima Nabe (fat tuna and green onion hotpot), Chanko-Nabe (sumo wrestler's food), Fukagawa Meshi (clam rice), sukiyaki, tendon, etc.
You should difinetely try Sushi. I guess you can taste not so bad sushi in any suhi restaurants in Tokyo. In case you don't prefer low fish, some sushi restrants rerve sushi with cooked food.