Tokyo is a huge city. In my opinion, NYC doesn't fully compare. Check out places like Shibuya/Harajuku (shopping, for young), Shinjuku (for young), and maybe Odaiba, Ginza and Akihabara (electronics area). If you can, stop in Yokohama for a bit and then you can get a Bullet Train ticket on their JR Line and head down to Kyoto. It's a lot smaller but it has a lot of historical sites, like shrines and temples. If you can get to Hiroshima, make sure you stop at the Atom Bomb museum, it's like a dollar or something to go. It's a really good exhibit and I think every American should go to museums like that. I got chills when I went.

Japan is generally a really safe place so there's not much to worry about. People are busy but they're also very nice. The main thing I'd say to look out for are the foreigners. There are some Russians, Africans, and such that are pushy and seem like they're up to no good. It's too bad that outsiders mess up the place. Everything is very efficient and prompt there, so make sure you're not lazy about things like getting onto the subways. You'll find that Japan is very advanced and probably wonder why the US doesn't have the stuff they do. I swear, when I arrived back in the US, I felt like I traveled back in time. No joke.