It is easy to say what is the Japanese traditional food but it is difficult to say local specialty of Tokyo. Tempura and sushi are definitely traditional food of Tokyo but you can eat all over Japan.
For example, okonomiyaki is local specialty of Osaka and Hiroshima, which both cities dispute each other about the originality. Monjayaki, which is similar to okonomiyaki is definitely a local specialty of Tokyo, especially in Tsukishima district which is not so far away from Ginza district.
Monjayaki is more snack kind meal than okonomiyaki which is a proper main dish. The dough is more smooth than okonomiyaki, contains more water. Then there are more variations of ingredients, cabbage is not the main ingredients as okonomiyaki.
If you want to try monjayaki, just watch out that monjayaki cannot be found easily outside of Tokyo. May be it is harder than finding Indian cuisine in a village of Japan.