A typical teenager in Japan spend their time after school and weekends at Harajuku. I spent so much time in Harajuku when I was a teenager.
Walk along the famous Takeshita Street. You will find lots of Japanese teenager busy for shopping and eating. Buy a crepe like a local Japanese. You will find various creative crepes with cheesecakes and ice cream in it!
Hub Japan has an article introducing things to do in Harajuku: