http://en.wikipedia.org/wiki/Tri_bandTri-band usually refers to the GSM 900/1800/1900 MHz band phones commonly sold in Europe, not the latest 3G frequencies (which just recently started to become available in the USA, and use different frequencies vs. the rest of the world.).
Regular GSM tri-band roaming will be okay in Europe, USA, and most Asian countries, but not Japan.
Here, you need a 3G phone that has 3G WCDMA 2100 Mhz band to work in Japan.
Such include the Samsung Z510, Z540, Nokia N95, 6233, etc.
You can find more at gsmarena.com - phone finder
Keep in mind - EU/JP WCDMA 2100 (Band I (W-CDMA 2100)) is not the same as that used in the USA by T-Mobile's 3G (2100+1700, Band IV). Thus, you cannot use a T-Mobile 3G USA phone in the USA unless it specifically supports Band I WCDMA 2100. This is when having a multi-band 3G frequency phone comes in handy - so you can roam worldwide on the 3G networks rather than on basic GSM.
I've roamed into Japan with a Nokia 6233 and Samsung Z540, and they work fine for sure.
----
Credit cards for cash?
Good luck!
Debit cards work well in most large city Post Office ATM's - no problem pulling out cash this way.
But really, you should bring at least $100-150 USD per day in cash to Japan in the first place - conversion to Yen can be done at home or in Japan. Otherwise, you'll be hunting down ATM's instead of vacationing.
Now, most major hotels, shops, etc. will take credit cards for purchases, so the basics of hotel + shopping is easily taken care of with a credit card.
Keep in mind that the trains typically take cash, so if you don't have Yen, it'll be tricky getting around by trains.