I could write a few pages on this topic but I'll keep it to some short tips:
1) TRY and speak the language, as long as you put forth the effort it will be recognized and everyone will be friendly.
2) Go to a karaoke bar... I know that sounds kinda crazy but you will be the fucking STAR. You can sing better than a Japanese accent singing American pop songs... they will LOVE you and most likely everyone will be buying you drinks trying to get you to go back up there and sing more songs. Seriously, it's a blast...
3) If you're in Tokyo if a club called Gas Panic is still around, GO! Specifically if you're single. It's where all the out of country models and Japanese chicks go when they're looking to meet American guys... well worth your time.
4) Also in Tokyo you MUST visit the Harajuku district... it's where all the cosplay crowd and gothic lolita scene is, very cool, bring your camera.
5) Obviously if you're a sushi fan... now's the time to indulge! Fork over the cash and try some fugu too... probably the safest place to try some
6) Hit up a public bath house... it's a really cool experience!
7) Stay at a Love Hotel, they fucking rock and you can even get rooms that are themed
8) I would recommend visiting Kyoto Japan for all the of the temples and zen gardens in the area... a bit away from the city but worth every minute!
9) Here's some things to try that you can't find over here:
Daifukumochi ... or really any kind of Mochi they have ice cream mochi even.
Taiyaki ... the look like pancake fish and are filled with sweet bean... fucking awesome
Kobe Beef ... sure you can find it in the states as well but get the real deal while you're there, I'm a sucker for a good filet :D
Imma bail on this list here... so much to write about, hahah
10) If you like video games at all... stop into one of the million arcades if for no other reason than to people watch and experience some culture shock :D
11) Pachinko! Fuck yeah, so much fun... learn how to play before you go and know that the machines are rigged to pay out more money Friday and Saturday during the day... It drives up word of mouth advertising and brings more people in for the big nights... When/If you when and you cash out they'll give you some kind of token... Because of gambling laws you'll have to take your tokens to another building (usually right around the corner from the pachinko place) and redeem the tokens for cash. TONS OF FUN!