UPDATE – Tsukiji Chūka Soba Inoue is currently closed due to a fire at Tsukiji Market. (Aug. 2017)
Our favorite ramen at Tsukiji is Inoue. This tiny stall that has standing only tables for dining has been in business for fifty years. There is only one bowl that is made from (I believe) chicken and soy sauce broth, has thin noodles, and is topped with slices of pork, menma (bamboo shoots), green onions, and kaiware (daikon sprouts). The soup is light and a good start to the morning.
This is a great start to the day, and in our opinion, better than having sushi for breakfast at Tsukiji as many of the sushi shops have become very touristy. There is usually a line here, so stand in line, order quickly, as the shop is run much like the Soup Nazi from Seinfeld. Stand and slurp quickly, and then move on to make room for the other diners.
Tsukiji Chuka Soba Inoue 築地中華そば井上
Chuo-ku, Tsukiji 4-9-16 中央区築地4-9-16
5:00 a.m. – 1:30 p.m. closed Sunday, holidays, and Tsukiji holidays
Food Sake Tokyo 
I remember this place from our last visit to Tokyo (~5 years ago I think). There was another place near there with standing room and tables on the sidewalk that serves what looked like beef stew over rice that looked good; we wanted to try it but the ladies running the place refused to serve me and my wife for reasons unknown to us … so we had ramen instead.
Oh no. Did you try taking her photo? If so, maybe that is why she refused you? She is a tough cookie. Her shop is called Kitsuneya.
https://foodsaketokyo.com/2016/03/07/tsukiji-kitsuneya/
I hope you enjoyed the ramen.
I don’t remember taking a photo and I can’t find a picture of that shop on my iphoto album of that trip. But it is possible my wife did, because she takes photos of everything …. Anyway, maybe we will give it another try next time. Btw I agree with you that a bowl of noodle is a great way to start the day. I used to eat noodles every morning when I was in high school in Taipei.
Next time you go, wait until you’ve ordered and are eating to take a photo. May the force be with you! 🙂