few questions, will you be more into sightseeing? do you want to just take in the experience of tokyo? do you want to go shopping? what is your budget for hotels? i've stayed at some decent ones for 7000jpy/night. how many different towns / cities do you want to go to? i've been to japan about 15 times at this point. can you or your friend speak any japanese? just a little bit will give you an exponentially better experience.
For tokyo, Ueno is definitely cool. check out ameyoko-cho if you're into street shopping for cheap goods that are decent quality. knockoffs and real deal stuff can be found here. It's what you would think of a typical asian outdoor market, except that you're in japan and it's alot cleaner than you would find in other asian countries. there's also a great microbrew bar a few subway stops away from ueno.
good shopping in shibuya, ikebukuro as well. check out some neko cafe's lol. i've been to the tokyo tower and it sucked. it was one huge ass line and i was mobbed the entire time. also pricey. you can get a better view at the government building, and it's free. haven't checked out the sky tree yet, but i have a feeling it would be the same way. skip anything in roppongi, it's a tourist trap.
tsukiji market is really cool to check out if you're into food culture. great places to eat around there too after you walk around in the morning.
if you're into ramen, the shin-yokohama ramen museum is pretty awesome. (someone incorrectly mentioned it as the tokyo ramen museum earlier, but yokohama is a 20 min subway or train ride away from tokyo)
if you go in august you can climb mount fuji. it's painful but not that bad.
also spend time in kyoto, it's just plain awesome. this is kinkaku-ji i believe.
Also, Yen is cheap so the dollar can go far. Ueno has some great spots to eat...
not quite true. yes it's been better the last few months, things are still expensive over there. i remember when it was 120 yen to the dollar, and the last few years it's been 70 to the dollar which was butt rape. now it's about 95 to the dollar which is sort of ok but still not good. a beer in tokyo will run you 800-1200 yen.