I've been to Japan twice (2005 & 2006) and have spent a total of about 10 weeks working in Tokyo and traveling solo around the rest of the country. The hotel I routinely stayed in in Tokyo overlooked the busiest crosswalk in the world, outside the Shibuya metro station. It was mind-boggling - I don't think I've seen so many people crossing a street at one time in my life. And this happens every other minute:
http://www.youtube.com/watch?v=QXtOdSgf6Ic
The hotel I stayed in, which overlooks this chaos, is called the Excel Hotel. Nice place to stay, if you have the money - very centrally located in the heart of the Shibuya action.
Japan is, in my view, one of the easiest countries to get around in because of the train system, which is the best in the world, as far as I'm concerned (and I've traveled extensively throughout about 40 countries). The bullet trains are clean, comfortable and on-time to the second (literally) and the feeder lines are reasonably comfortable and always on-time as well.
Obviously, you need to spend some time in Tokyo and Kyoto - Tokyo as the massive super modern city of today...and Kyoto as the city of yesterday with all the beautiful shrines and temples (I'd allow 4 days for Kyoto alone). And as long as you are in the neighborhood of Kyoto, you may as well do Osaka and Nara. I particularly liked Nara, with all the deer all over the place.
I would highly recommend Hiroshima. It's a sobering trip, to be sure...but it's a must see, IMO. And while you are there, you can go to Miyajima (where the gate in the water is that is so often photographed - beautiful).
I also quite liked Nikko (north of Tokyo and in the mountains), Kamakura, and Mt Fuji (you can go to hot springs in addition to seeing the mountain itself more 'up close') - all are reasonably close to Tokyo. And I also really like Himejii (where the 'famous' Samurai castle is, with beautiful gardens right next door) and Omomichi (a very small town - don't expect any English here).
Get yourself a Lonely Planet guide to Japan and save up your pennies, because Japan is extremely expensive. When I was there, IBM paid for my hotels & meals, even though I traveled for fun on the weekends, thank goodness. I only had to pay for the three weeks out of the 10 when I was on vacation. But even then, over the two trips I spent several thousand dollars on train passes (have to buy these before you leave), hotels, and food.
If you have any specific questions, I will try to answer them.

I do not speak Japanese...but I easily got around without difficulty, so you should have no trouble at all, knowing Japanese.