That depends on your idea of a good time. I lived in Tokyo during my teens -- went to an int'l high school there -- and still visit often as my parents still live there. Roppongi, if you just like poking around and seeing stuff, is perfectly harmless for a 16-year-old and offers a lot of good photo ops. It is also a "gaijin ghetto" as the U.S. Embassy and residential compound are just a few blocks away so there are lots of foreigners around in the evenings.

Where else in Japan are you going?