meet people, go to bars even if you don't drink. met some very cool people and even a travel buddy who took some days off work to slum around with me and my brother just because he could and showed us the area he was from and all the cool places to hit.
make sure to make a trip to a sizable grocery store and a store with a section devoted to kids and candy and such. i think its called a niki. get a bunch of weird shit and have a blast trying it all.
visit a hotspring and act really immature about being naked with other men and constantly trick each other into getting a face full of wang "Holy shit dude look at that!" (penis in face).
go to a karaoke joint. its unlike anything i've seen in the states. here its like you go to a bar and then sing or whatever its not a main thing. there its like going out to a movie or going bowling. you get your own little room with some fancy touchscreen song selection controller things. rooms are sound proof with excellent sound systems. free drinks.
if your friend knows of a good place, go somewhere to experience a kaiseki. when i was in japan my "japanese mother" took us to an amazing place that was a pottery display/kaiseki joint set in an old grain storage building converted into the restaurant (which was awesome because it was hidden away in the middle of a very modern neighborhood which made it slightly magical) and she was close friends with the wife of the owner who does the full on tea ceremonies so we had the major hookups. the presentation and the courses and having her show us the proper way to do everything was extremely cool. i highly recommend it if you know of somewhere to go. you can order a kaiseki meal from many places but they'll often just bring everything out at once in bento dishes and leave you to it. it is so much better, at least one time, to go to a legit place that serves you course by course with all the proceedings and presentation.
maybe stop by an arcade if theres one near where you are. the games are expensive as hell, most are 100yen a play which was like a dollar when i went, but just being in the arcade is a pretty cool experience. also if the arcade has multiple floors, find the one with the fighting games or the quiz games and prepare to be amazed at the crowds and cheers.
if you can or if you're into it, don't forget to check out the countryside. i stayed in kyoto for a few days and while the city is nice and all driving out into the country side where the fields and rivers and such are to be found was fantastic. also look for any nearby mountains or hills as there are tons of neat trails with all sorts of cool things to be found wandering like shinto shrines and totems, graveyards, and other neat stuff you'd miss sticking to the cities.
stop by a fast food place like sukiya and try out some awesome vending machine style ordering. can't read japanese? no problem. push the button for whatever looks good (ignore the side options its stuff like adding eggs or green onion topping and such to your order), it prints you out a ticket and hand it to the cashier person. nothing like some delicious gyudon and miso.
