It is (finally!) possible and safe to use your credit card at most stores in Japan, although smaller shops, museums, and temples may demand cash payments. (A surprising number of Japanese taxis still take cash only, so be aware of that, too.)
I recommend my tour guests carry from 3,000 to 5,000 yen cash per person per day. That covers drinks, snacks, and incidental small expenses. If you find yourself in need of cash, nearly every convenience store in Japan will have at least one ATM that accepts Visa or Mastercard for cash withdrawals. Keep in mind that there is a small fee for each transaction you make, so it is advisable to withdraw larger amounts of cash at once rather than making multiple small withdrawals. (It is important to note that currency conversion rates are determined by your credit card company, not the ATM itself. )
Japan also utilizes a wide variety of Electronic Money cards (IC cards), so see my separate post on those! In addition, there are now dozens of different payment methods available using your smartphone. Since that's something I prefer not to do myself, I'll leave those up to you!
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