The fish market. It's done on such a huge magnitude, it's like nothing you've ever seen. The only problem is you'll have to get up stupidly early to see it!
Spend a night in one of those capsule hotels too, that's quite an experience.
If you're cheap, check out the tall goverment building. You can go to the top of a 50 storey building for free and take in the 360 degree view of the city. Don't waste your time and money on that Tokyo tower thing.
Roppongi is quite the night scene I agree, but it's very pricey.
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