This complex is so big you can take guided tours around the thing. But the most amazing thing is the Tokyo City View. There is also a Sky Deck that is open if weather permits it. The City View is 1500 yen, plus Sky Deck it's 100 yen more, students pay 500 yen less. It might be more expensive than most other attractions but it's worth it. The Mori Art Museum is up there as well and is included in the price.
I went there when it was already dark, when you're up there with Tokyo al dressed up in neon lights around you, you realise how mindboggling big this city is. The only dark spot is the sea.
It also has a restaurant floor, I think it’s the 5th floor, a cinema and a lot of shops.

Roppongi Tower is a must to go to if you wanna see what Tokyo is all about. It is a great look out and well worth the 1000 odd yen to get a gander.