Even though there are plenty of restaurants in Tokyo, there are not many places which open till very late. However, the problem has been resolved since the opening of the Yokocho in Roppongi. It is the largest yokocho (food court) in Japan which gathers different cuisines from the world.
There are 20 restaurants inside Roponggi's Yokocho which serve different types of food such as sushi, yakitori, yakiniku, alcoholic drinks as well as western and Korean food. The operating hours start at 5pm and it opens till very late at night. For Friday and Saturday, it even opens till 5am. Perhaps you can try visiting this place if you happen to be in Tokyo.