*** Katou has closed with the closing of the Tsukiji Jōnai Inner Market and has moved to Toyosu Market. It is in the Suisan Nakaoroshi Uriba-to on the 3rd floor and the name changed to Ikinoya (粋のや). I believe it is being managed by Kaisendon Oedo, another popular shop that moved from Tsukiji to Toyosu. (updated 10/21/2018)
For a truly local breakfast at Tsukiji, bypass all of the sushi shops and follow the fishmongers to shops like Katou. The menu consists mostly of grilled and simmered seafood served with rice, miso soups, pickles, and a side dish.
Kinmedai, 金目鯛 splendid alfonsino, when simmered in a sweet soy broth, will melt in your mouth. I was lucky and got the head part of the fish, while my neighbor got the tail end. Dig into the head with your chopsticks to pull out small nuggets of tender meat. The eyeball is a delicacy. It is a challenge to pick up with your chopsticks. If you are successful in getting it into your mouth, suck up the tender collagen, but be sure to spit out the hard white part.
Katou’s big menu includes Saikyo miso marinated and grilled black cod, an assortment of seasonal sashimi, and seasonal whole fish simply salted and grilled. The bowl of rice is hearty, for the fishmongers who work in the market. It is impolite to leave rice in your bowl, so unless you are very hungry, it is good to ask for a small bowl of rice. In Japanese, gohan o sukuname.
Chuo-ku, Tsukiji 5-2-1, Building #8 中央区築地5-2-1ビル8号
This Tabelog page shows some of their other main dishes: