Unfortunately, I don't know well about good restaurants in these regions. One place I remember is Tsukiji fish market. There are lots of places to eat near the market, but you should try to go sushi places INSIDE the market area. There are multiple sushi bar there. I can't tell which one, but you can go to the place with the longest line. When I was there, I had to wait for 1 hour or more in line. But it is worth it.
In Tokyo, you should try good Soba (buck wheat noodle) at least. In Osaka, you should get Takoyaki (octopus ball) and Okonomiyaki (savory cabbage pan cake). In Kyoto, maybe Yu-doufu (boiled tofu) and Shoujin-ryouri (monk food).
Then, there are a couple of chains, which you might want to check out. For Japanese fast food, you can try Yoshinoya (gyu-don, beef ball) and Mos-Burger (McDonald like place, but you probably find it interesting). My wife was pretty excited by a chain restaurant Pomu-no-ki (
link). I was pretty impressed by it, too.
There are lots of Ramen, Udon, Soba shops, too. Also, you should try Japanese Curry shop.
Also, check out the food section of major department stores (e.g. Mitsukoshi), there will be lots of regional food sold for gifts, and they usually have lots of free samples.
In Tokyo, I was blown away by shaved ice. The texture was something else, and I've never thought that shaved ice could be so soft and yummy. The owner was very enthusiastic, and explained us the art of shaved ice. Unfortunately, I don't remember the location. After I came back to AK, I had to search for a high-end shaved ice machine. But it is a bit too expensive.
Sorry, I don't have specific restaurants. Hope you'll have great time, and please let us know how it goes!
