I also wouldn't bring outside food in; consensus. But the comments about no izakaya, counter seats at ramen and sushi bars being no go areas, the suggestion that children don't eat at upscale restaurants and that at 21 months they only eat some of what grown ups eat contradicts (violently) my own direct experience. So from that perspective...
Like with mkjr's kid, the more expensive the food, the more it was clamoured for, particularly when she was very young.
I took her to Nakajima in Shinjuku when she was two and a half for the 800yen lunch time menu. At that time of the day it's a classic example of somewhere that doesn't cater to children and relies on a fast turnover. I got the fried sardines for her thinking they would be more appealing to a young palate. I chose the more lauded option; sardines boiled with ume. LapChild tasted mine and wolfed them down, leaving me with the not so sensational fried versions. I quickly learned my lesson.

Had to obscure faces and don't have photoshop, but it gets the idea across: us and another family (with a 1 yr old) having lunch at an Izakaya in Kichijoji - En - https://tabelog.com/en/tokyo/A1320/A132001/13009990/ (this place fits in well with a visit to the Ghibli Museum)
And here's a photo taken by En's owner of the same room: https://tabelog.com/imgview/original?id=r4195944034841
Izakaya can be some of the most accommodating and comfortable places to eat as a family. They vary widely, so don't count on them but definitely don't rule them out.
EDIT TO ADD: Found this article about a particularly child friendly izakaya chain:
http://bestlivingjapan.com/kid-friendly-izakayas/ (As I said, they vary. Wildly.)