ah, meant to reply to this earlier.
ok, 3 days, let's see.
if you don't know where to stay, i can recommend a hotel called "St. Hills" in Ochanomizu - http://www.sthills.co.jp/englishmain.html Very nice staff, adequate rooms and good prices. just up the road from Chuo Dori, the Marunouchi subway line and Akihabara. i look to stay there each time i go to tokyo.
stuff to do in three days, well i'm going to make some assumptions about what you like and your ability to get around.
1. you MUST go to Akihabara (not hard if you stay in St Hills). the epitome of tech. walk up the road then to Okachimachi for Ameyoko. lots of little stalls for food and clothes. great place to buy sneakers too (i'm a sneaker freak). if Okachimachi is not your bag, you can instead walk the other way up to Yasukuni Dori and go to Yasukuni Jinja shrine. great and poignant war museum. see the Ohka suicide plane. marvel at how the same firm that once made Zeros now makes Lancers.
2. you MUST go to Shibuya. lots of clothes stores, music stores, good youth culture. then walk up the road to Harajuku. visit Meiji shrine if you want 'old skool' culture. this whole area will blow your mind.
3. Shinjuku is also not bad. very big but worthwhile.
other bits
- i advise you to do stuff you wouldn't normally do. some stuff may be odd, but that's half the fun.
- buy drinks from the drinks machines - pocari sweat, calpis and that.
- TRY RAMEN. AND GYOZA. the little tiny food places are unreal.
- if you go to Harajuku, walk down to Omotesando. There's a sushi shop about half way up the street with heavenly sushi.
- take a camera!
i would probably avoid roppongi. i think it's always been a bit of a dump and even the addition of roppongi hills doesn't really help. interestingly, it's the foreigners that ruin it. but that's just my opinion.
i am F****ING jealous that you are going. You will have a fantastic time!