7-Eleven Stores: most 7-Eleven stores throughout Japan have ATM machines. Visa/Diners/American Express are accepted, although they state that "some cards bearing these insignias may not be accepted", and there may be a charge (from your bank). Note that Mastercard is not accepted.
For details, see Seven Bank Ltd.

Post Office & Citibank: ATMs can often be found at these locations, and are a handy way of getting cash.

VISA: If you're particularly anxious about knowing where VISA cash machines are, I noticed that they have a website which lists all the locations. Go to the VISA ATM Locator, input the city or town, and it will list all the addresses where ATMs can be found.
You could then even see where each one is on a map: go to Diddlefinger's maps with English labels, choose "English Address Search" and put in the relevant parts of the address. You could even then save the link to that map on the Diddlefinger website, or copy & paste the URL into normal Google Maps.