It is still difficult nowadays to find international public phones, especially outside major centers, such as Ginza or Shinjuku. There is a trick to bypass this annoying limitation; just use a prepaid international phone card for which you have to dial a local number, enter your code, then be redirected overseas.
You can buy phone cards and use fax, photocopier and more at the ubiquitous convenience stores ("combini"), such as 7Eleven, Family Mart, Sun Kus or AmPm.
For the Japan Telephone Directory, check TOWNPAGE.
