Serious Eats - seriouseats.com

Why can't I ever make a short post?

I really don't think you can go wrong with eating in Japan. Even their convenience store food is good! I just recommend eating everything that looks new and interesting. Eating well in Japan isn't necessarily expensive , either.
I gotta recommend going to an okonomiyaki joint in Osaka, though. They're rather well known for that particular dish. Making your own with a bunch of friends and a cold drink at your side, there's nothing like it.

I guess the most high end place I ate at was Yasaiya Mei in Shibuya, Tokyo. Mostly vegetable-oriented, so its good for any vegetarians you might be traveling with.
Exceptionally friendly and attentive service, you can get by with extremely limited Japanese (hitotsu - one, futatsu - two, hand signals and the like).
The food is artfully presented, interesting (but not bizarre) takes on traditional foods. This place seems to epitomize the clean, fresh flavors and aesthetics of the ingredients they use.
Their lunch menu is limited mostly to three or four items, but most of it are teishoka, or set meals. The teishoka you order may come with soup, rice, vegetables, pickles, tempura, etc.

Yasaiya mei is located in the brand new Omotesando Hills shopping complex in Shibuya. The complex has a lot of interesting boutiques and tons of restaurants and smaller food shops like a gourmet chocolate boutique and a really exceptional gelato place called Gelateria Bar Natural Beat (try their Sea Salt Caramel with Caramelized Nuts or the Bellino with Swiss Meringue and Homeade Limoncello), so its a nice place to stop by and have a light meal and a snack before heading out into the rush of the hectic Shibuya shopping district again.

http://www.bento.com/tokyofood.html
Here's a great English-language site with restaurant listings and reviews from all over the Tokyo and Osaka area. This is where I found Yasaiya Mei, so hopefully you'll find somewhere that piques your interest, too!

If you want to visit the Tsukiji fish market, I highly recommend Nakamura-san and Yoshino-san's guided tour. You can read about it here: http://marriedwithdinner.com/2006/02/03/worlds-freshest-sushi/
They gave us great recommendations for where to eat sushi after the tour.

There are about a dozen different regional varies of ramen on offer at the Shin-yokohama Raumen Museum (about 30 minutes south of Tokyo by bullet train). You pick your meal from a ticket machine outside, usually with helpful photos.

Also in Yokohama: Katsuretsu-An, Japan's oldest tonkatsu restaurant. If you don't read Japanese, this may be a challenge -- I didn't see any english menus and even the prices were in characters, not numerals. We were with a Japanese friend and she ordered for us, thankfully.