Here are the Japanese places I recommend. Except for the last place listed, I’d get a Japanese person to make the reservations and print a map.
(1a)
Sushi-- “Sukiyabashi Jiro” They only have one course menu, so it’s easy. It’s the best sushi in Japan, period. If you like sushi.
Tel. 03-3535-3600
(1b)
Tempura-- “Kondo” It’s also a tiny counter place, but the best tempura, period. If you like tempura.
http://gourmet.yahoo.co.jp/0000607394/P055083/
Tel. 03-5568-0923
...My recommendations are the following, however, since you guys are in Japan you might as well start with the full-on Japanese course menu called Kaiseki consisting of 6-10 different small plates of seasonal dishes.
(2) “Komuro” -- in Kagurazaka.
http://www.brutusonline.com/brutus/regulars/gourman/shop.jsp?issue=186&backTo=list.jsp
tel. 03-3235-3332
Authentic Japanese kaiseki food. My personal preference is always the more sublime cuisine of Kyoto, but I think that Komuro is definitely one of the best in Tokyo— the chef has the magic touch. I think they have two dinner courses, both exquisite and in my opinion much better than the (even more) expensive stuff that’s too-well known. It’s in a back alley of one of my favorite neighborhoods-- the former geisha quarter in Tokyo where I used to live. Quite classy and quiest. But it’s hard core— this is where I’d take you if I were with you.
(3) “Kozue” in Park Hyatt hotel, Shinjuku.
http://www.parkhyatttokyo.com/hyatt/dining/kozue.html
This is really really good food— like the “Komuro” place above, but also accessible to Gaijin. I took my Insead friends here, and they all loved the food— even people who had never eaten real japanese food before. Not bastardized, but also they are used to foreigners so it would be easy to go here if you don’t have a Japanese guide. Also, the match between the Japanese kaiseki course cuisine and the endless cityscape of nighttime Tokyo is amazing. I definitely recommend this place.
Go wild.