It used to be that places that accepted credit cards in Japan were quite rare. Things are slowly changing (Japan is still very cash-based) but most major chain stores accept credit cards. Unlike in the US, where you have a payment terminal in front of you, in Japan you always have to hand over the card to the cashier, so you can’t use that to determine if you can/can’t use cards.
Basically, the best advice is that, if the shop is a major chain, it will accept credit cards. Lawson, 7/11 and Family Mart all take credit cards. Major sit-down restaurants might, but family restaurants probably will not (Saizeria, Gasuto [Gust], and Friendly, for example). McDonald’s and places like Yoshinoya, Nakau, and Sukiya don’t accept credit cards, but, on the plus side, Starbucks does (now if they would only sort out the wifi thing in Kyoto). Note that in Kyoto, Fresco, a supermarket, does not (many smaller supermarkets don’t, but bigger places such as Life, Kansai Super, and Aeon do take credit cards).
In general, you can use credit cards to buy more expensive train tickets (such as Haruka or Narita Express tickets, and Shinkansen / Bullet train tickets) but not regular tickets. Some taxis accept them, but others won’t – it is best to check before getting in (hint: when the driver opens the door, show a card and say “OK”).