Most ATMs will not accept your cards. However, as you’ve already discovered, 7-11 ATMs should be fine as long as your cards use one of the international systems like Plus or Cirrus (the logos are probably on the back of your cards). I say should, because there can sometimes be problems with compatibility even if the system says it can accept your cards. Other options for getting cash are the post office, Lawson (I think their E.net ATMs accept foreign cards) or Prestia. Prestia operate the former Citibank network so if all else fails, I’m pretty sure Prestia will work.
Also, if you’re flying into Tokyo, their are 7-11 (more correctly 7 Bank) ATMs throughout Haneda and Narita airports.