Shibuya
Shibuya is known to be a hangout for younger people but anyone can go to Shibuya and enjoy the sights. Of course, you have to meet your friends at Hachiko, if you haven't watched the movie its the most famous and loyal Japanese dog and a real tear jerker.
There's also Yoyogi park and when you get tired of walking around and night comes around you can enjoy Nonbei Yokocho aka "Drunkard's Alley". Basically a little strip where a lot of bars are and you can drink a lot for really cheap!
And you have to sit around and watch Shibuya Crossing (picture) for a bit to see the most people you will ever see cross the street at the same time.
