Is www access a necessity (like it's for work, etc.)?
Most modern hotels have coin-op PC's. Ditto for semi-communal "mansions". If it's just to check your e-mails, log onto MCB, etc. then it might be worth it to just get your travel agent to look into internet accomodations before you book any reservations.
I think I paid 500Y per 10 minute sessions when I was last there (Fall 07). Less then $4.50/10 minutes at that time. OK for a quicky e-mail check, but not long enough for a surfing session.
The only problem would be if you lack even basic language skills as the homepages will be in Japanese and such. So just finding the search engine might take a little bit of trail and error. Also the keyboards most likely will have hiragana text on them, further complicating your typing if you toggle back-n-forth accidentally from Japanese to English.
Internet cafes are also an option.