Since the early 2000's Japan has been moving from a cash-only culture to a card culture and it is now easier to pay for large expenses with a card (hotel, shopping, …) but most of the daily expenses will be paid cash, and getting cash can still be hard.
Don't shun the ATMs and change booths at the airport.
Forget about the ubiquitous ATMs in convenience store. As of 2008, when they say "visa accepted", they mean "domestic visa".
Citibank however has 24-hours ATMs a little everywhere in Tokyo, and they do take foreign cards – http://www.citibank.co.jp/en/atm/index.html
Your best friend throughout Japan still is the Japan Post. Almost all their ubiquitous offices (look for the red T sign in the street) have gaijin-friendly ATMs (look for a green clover mark near the post entrance). Beware, however, of opening hours, as well as Saturdays and Sundays, when a lot of the offices - and their ATM - are off limits.
This tip has the address "Post office, Citibank, Airport"