With respect to the other reviewers, I find the best place to view this bridge is from the deck of the booze cruise leaving from Hammamatsucho. Other that how it looks from the deck of a boat...what can you say...it's a bridge. It goes across the water and cars drive on it. There are lots of pretty lights. But honestly, all the coolest cities know that you aren't really a city without a rockin' bridge. And considering this one revolutionized the commute and flow of traffic for millions of people, it is worth a look.
The building itself is a beautiful example of architecture. And this building is a one-stop shop of anything bureaucratic. Literally any government function you can dream up can be found here. Very popular tour destination in the heart of the skyscraper district in Shinjuku. But if it's a view you're after, Roppongi really is a better bet. Especially since there is usually a pretty lengthy line for the elevator up to the top.
The Monet of tourist attractions: cool from a distance but a total let-down when you see it up close. It is nothing more than a radio tower surrounded by stinky tour buses with a pathetic shopping center crammed underneath it. The only people who actually go here are tourists who allow Lonely Planet to jerk them around and foreign guys who think their Japanese girlfriends actually want to go here. Let me clue you in: IT'S NOT THE EIFFEL TOWER, DUMMY! There is absolutely nothing romantic about a giant orange radio antenna. If you want play off of a city view, don't be a stingy schmuck: go to Roppongi Hills.