Given all the sushi and Japanese-cuisine-related answers, a different perspective:
The Japanese are notoriously good at taking American cultural artifacts, and then making them so much better than we do over here, it’s nearly shameful.
To that end, I would say that the best place to eat in Tokyo is at one of Tokyo’s many burger-focused eateries… After you’ve indulged in sushi, and all other “traditionally Japanese” foods, after you’ve tried some interesting spins on French and Italian cuisines/fusions, there’s really nothing like a nice solid “Hamubaaaaaaaagu” to reset the palate, and ready you for further exploration:
Not exactly a traditional American presentation… But after a nice long walk through some temples, nothing quite hits the spot like a couple artery-clogging cheeseburger patties – perfect medium rare, still sizzling on a metal plate. Honestly? It’s really hard to get stuff this good stateside. Japan wins again!
I’d also like to put in a good word for Sekai-no-Yamachan, an izakaya-style restaurant that specializes in really really great tebasaki chicken wings.
(Photo Courtesy of: http://www.flickr.com/photos/kya…)
Ideally, you’d want to visit the headquarters in Nagoya, but the Tokyo wings are nearly as good, and highly addictive. If you consider a rollicking good booze and bar-food-fueled night out with friends a key component of a great meal, Yamachan should definitely go somewhere on your list. For those with cashflow issues, it’s also fairly inexpensive.