I went to Tokyo when I was 16 by myself. Now THAT was an adventure.
It is a really great place to visit, and I myself am going there to teach when I graduate in about a year or so. I have been planning to do this since I was 16 and I'm 25 now. However, teaching required me to complete college which I wasn't planning on originally. Plus my parents prefer the trickle down method of raising.
Kick you out at 18 and live life happily while the realities of adulthood trickle down.
Anyways, I'm finally prepared to go and I have made a few connections. Here are some things to consider.
Try to pick up the language. Buy a book before you go anywhere, a beginners textbook should be fine.
Tokyo is super expensive, keep in mind that nearby countries are very very cheap and worth a week long trip.
Scout out youth hostels. Mine was someone's home. An american lady and her japanese husband rented out rooms to travelers but there was a 10pm curfew. Fortunately the prices are about 30$ a night so you can do that for a week to save money. Plus they will often include actual japanese meals, so that is pretty cool.
You will probably be set up with an apartment. Just try to enjoy yourself and really get immersed in the culture. It's amazing.
