Using Credit Cards in Japan
Will restaurants in Tokyo & elsewhere generally accept
I don't want to carry a lot of cash around, & don't have an
Many restaurants do not take credit cards. You should always be prepared to pay with cash. The possibility of a restaurant taking American Express is pretty low unless it's some kind of tourist destination or hotel restaurant.
I am still surprised by the number of transactions that are done with cash in Japan. I was working with a tour group one time, and when the operator bought our group train tickets he paid with cash that he had in his briefcase. ¥800,000!
I just got back from Japan, and like la2tokyo says, not very many restaurants accept credit cards. If in doubt, you can always check the Tabelog listing for the restaurant beforehand -- most listings will have some sort of information about what cards, if any, are accepted. For example, Wadakin does not accept cards even though it is quite spendy! (see where it says カード = 不可 )
I know you don't have an ATM card, but for those who check out this listing later, the only places where I could use my card was at 7/11 or any 7 bank-affiliated machines located elsewhere (say, a hotel lobby). I suppose you could purchase some AmEx traveler's checks and cash them in at Narita Airport.
Most mid- and higher-priced restaurants accept credit cards these days, although there are some surprisingly expensive ones that don't, so you should always check beforehand, and you should always be prepared to pay in cash just in case. Chain restaurants, and restaurants in office buildings, department stores and restaurant complexes almost always take credit cards.
Lots of restaurants do accept credit cards these days (many, many more than used to be the case not that many years ago), but many still do not. I also have a feeling that Mastercard or Visa is more often accepted than American Express, but I might be wrong. Check in advance if you can.
While in my experience most high end places in Tokyo do accept cards, it seems that a large number of high end sushi restaurants do not (e.g., Mizutani, where you will hand over 20,000 yen or more per person just for food) so definitely don't assume you can pay by credit card on the basis that the restaurant is very expensive.