I know this is an older post, but for anyone else that is deciding to go to Japan, here is my two cents!
You can definitely do Japan on the cheap while you're there. If you're flying over from North America it's freaking expensive though. I stayed in Shibuya for about $100 a night (I was at a conference, I think the regular price is more around $125-$150. I believe it was Tokyu Stay Inn. It was a smaller unit, but it was perfect for my needs. Had a washer/dryer, heated toilet, microwave, stove, sink, bed, tv, etc. Everything was a decent size considering I was in Tokyo.
A common misconception is that food is expensive there. If you're buying fruit and stuff, then hell yeah. To be honest though, I'm pretty sure fast food like McDonald's is cheaper over there than here. It can add up over time, but you could easily keep around $50 by eating breakfast/lunch/dinner all at restaurants. You can go to the supermarket and pick stuff up for cheap too. Bring a friend that speaks Japanese with you if you're unsure about ingredients.
Roppongi is a rough district. I went with 2 other guys and I got punched once, or twice, and harassed in the crowd a couple of times by Japanese guys. Japan actually has a fair amount of racism, and when you're a white guy stealing all the chicks on the dance floor, they will take notice. I had one bartender refuse to serve me. I was at, "A-Life," in Tokyo, in Roppongi. They tried scamming us by buying a table (shitty, wooden table with 4 rickety chairs) for $1000. Yes, that was the actual conversion to US$. Regardless, I had a great fucking time and I wouldn't have changed it for the world. And no, we weren't stupid enough to buy the table, although we could have afforded it.
I was only there for a week, but I heard Roppongi is great for picking up the younger crowd. I forget what the other age groups for districts were. If you're into cougars, then I heard Ginza is the place to be though.
Akihabara is probably the coolest district. You could easily spend a week there sifting through old shops finding weird and interesting things. There are all kinds of professional stores, to run down shacks, or places that might double as a living space and store tucked away on the third floor of some apartment building.
One word you need to know for your trip is, "Sumimasen," (Sue-Me-Maw-Sen) -- say it quickly. It means, "Excuse me." It's crowded and sometimes you bump into others. Stay on the right hand always when traveling underground on escalators, or subways, etc. It's kind of the silent code, so that everyone can get to where they are going quickly. Otherwise people will stare at you. A good tip for walking in large crowds is not to look at anyone, just focus on where you are going. If you stare at anyone you're going to meet with them at some point and do the awkward right-to-left shuffle. That's not fun when you're trying to get where you're going and there are thousands of people around you.
Unless you have a huge group, stay out of Roppongi. Visit pubs instead of clubs, unless you're looking for something else. If you walk around certain parts at night be prepared to be solicited by 50 hookers on the way back to your hotel unless you have a girl with you.
Anyway, that's all I can think of for now. Have fun! It's an exciting and weird place.