Favourite Eateries?

Are there any good food places or individual dishes in Tokyo / Kyoto you would like to recommend?

.. Also, if anyone knows how I can say 'Is it vegetarian?' in Japanese I'd love a short lesson!

Maisui restaurant is one of my faves in Tokyo. I try to go each time I'm there. It's Japanese-Korean fusion. I don't eat meat, but I do eat fish. This restaurant has a good amount of non-meat and non-fish items, each ordered individually (tapas style). Best potato pancakes I've ever had.

http://metropolis.co.jp/tokyo/443/restaurants.asp

Vegetarian can be as simple as saying "vegetarian" if you're in the big cities.

Great, it's nice t have at least one recommendation. If we find it, we'll go. I'll let you know what we think!

Not too familiar with vegetarian places, but I'm sure you can get veggie Okonomiyaki. I enjoyed the okonomiyaki that they served in the Kyoto train station (bottom floor, near the rear bus stop). There's also a good one on the top floor of the building over the South entrance of the Shinjuku station.

It might be a bit expensive without the meat, but I found a shabu shabu/sukiyaki place that I really liked in Shinjuku, called Mo Mo Paradise. It's across the street and about a block further from shinjuku station from the main Kinokuniya building. (not the one in Takashimaya)

SaRabbit said:

Are there any good food places or individual dishes in Tokyo / Kyoto you would like to recommend?

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You can have a look at this address : Secret Japan - Tokyo Restaurants. It is a section of the Secret Japan forums containing about 200 reviews of restaurants found in Tokyo. There are also some information on (good) chain restaurants.
The number of restaurants in Tokyo is really astronomical, and you are sure to find some places that will suit you - and this is one of the best things Tokyo has to offer, IMO.
sanji