Well, I've been back since Friday and I guess it's time to share some recommendations of some places I've found great food (likely all tourist traps, but still!

), in no particular order.
Katsu Midori
(Shibuya, Tokyo)
Great and inexpensive (for Western standard) kaiten-sushi in Shibuya (8th floor of the Seibu department store, 1 minute walk from the JR station). It has an English menu and it's super easy to order, both at the counter and at the table.
There is another Midori around the corner (in Shibuya Mark City), but this one has much less queue.
I'd recommend the chūtoro (medium fatty tuna) over the ōtoro (fattiest part of the tuna) as I don't like how they cut the latter here.
Mori Mori Sushi
(Horikawashinmachi, Kanazawa)
Randomly found in the Forus building, just outside the JR Kanazawa station, this place had the best ōtoro I've ever had.
Sumiyoshi Ryokan
(Honmachi, Takayama)
Not really a restaurant, but we had an outstanding stay in this ryokan.
The people here are super nice, and the old lady who brought us dinner was super jolly and fun and knew English far better than pretty much anyone else in Japan!
The kaiseki dinner served here was great, especially the Hoba Miso (basically food mixed with fermented soybean and grilled over a dry magnolia leaf) which was one of the best thing I've ever eaten in Japan.
Monsen Ramen
(Kawaramachi, Kyoto)
Just behind Ponto-cho, we found this little chicken ramen restaurant, run by young peeps with dyed hair and One Piece action figures behind the counter.
I can't remember exactly what I ordered (menus are in Japanese only), but it likely was what I supposed to be the most popular dish there.
And OMFG it was unbelievable. The chicken soup was so delicate, and yet so full of flavour. Probably the best ramen I've ever had (and even considering I'm more of a hot and spicy person)!
Yorozu Enraku
(Gion, Kyoto)
Sort of an izakaya kind of place, but quite upscale, with the whole traditional Japanese tables and all that.
Considering the location, is not even that expensive, and the glazed pork belly was unbelievable.
Nagataya
(Kamiyacho, Hiroshima)
This Hiroshima-style okonomiyaki shop was by far the best okonomiyaki I've ever had in Japan (even considering I like the Osaka-style more).
Also, it's just around the corner from the Atomic Bomb Dome, so it's easily embeddable in a half-day trip in Hiroshima, on the way to Miyajima.
Kikanbo
(Kanda, Tokyo)
Another great ramen shop, this time super spicy. You can choose your spiciness level (the hottest level requires 100 yen more

). We tried the highest free level and, while for my wife was too hot, I found it exactly on the limit between "great" and "fire covering all other flavours".
Ginza Kyubey
(Ginza, Tokyo)
By far the highlight of everything.
We wanted Jiro, but Jiro was sold-out half an hour after opening the reservations for September, so fuck Jiro.
Kyubey offers several sample menus, we opted for the most expensive one (15000 yen for 16 nigiri + soups and appetizers). Now, I'm known as a cheapskate, but fuck me, this was absolutely worth it.
When they served the chūtoro I was about to cry. It was nonsense, unbelievably better than any other sushi I could even imagine.
Try to imagine the difference of quality between your run-of-the-mill all-you-can-eat sushi restaurant and a good sushi in Tokyo (let's say the aforementioned Midori). It's pretty much the same difference that I found between Midori and Kyubey. It's something quite hard to explain, but I hope I managed to describe it well enough.
One warning though: Kyubey serves the "odori ebi" (dancing shrimp - or prawn, never got the difference

). "Dancing" because it's fucking alive when they bring it out of the kitchen. While it gets the right temperature, you can watch it while moves its legs and whatnot. Then the chef breaks it in half, he removes head and tail and put them back on the plate, where you'll see its fucking legs moving for a lot of time, until someone bring the plate back in the kitchen where they'll fry the head and tail and serve them back to you.
We knew about it and asked out of it, but the guys next to us ordered it so I could watch the whole thing horrified (while my wife, also ex-vegetarian, covered her eyes the whole time).
So yeah, if you are like us, when the chef asks you if you have any allergies, just tell him to replace the live shrimp with the ordinary boiled one (which was great, btw!).