Hmm. 6 days?
I'd suggest -
1. Semi-fast train to Niigata. Visit the warves and the Seiko battery factory. They're faulous in mid-summer. Some people say that in order to capture Niigata best you need to switch your camera to grey scale mode. I disagree with that. I think leaving it in colour mode will capture the exact same thing and give you far more nuances of grey across the city.
2. Take the coastal slow train up to Akita City and visit the famous Concrete Manufacturing Musuem. That's a very full day there so get lots of sleep!
3. From Akita, take an over night bus to Hachimantai in Iwate. It's a ski resort that is open in summer and you will get some fabulous senic views of the mountains of that branch of the Japan Alps, uncluttered by trees as they've all been cut down for the ski runs. On a good, clear day you can see Mt Iwate and hear the JGSDF artillery doing their practice firing at the active volcano. If you have time, you can climb Iwate san as well - remember not to climb the side the Army is firing on! (Oh, the laughs when that happens!)
4. Travel south to Sendai and visit the famous Sendai castle. Again, it's very famous and the center piece of a wonderful city that will give you a taste of the "real Japan".
5. You're running out of time now, so you'd best hurry back to Tokyo. The best way to do that is by over night bus. You'll see the most of Japan that way. Make sure to sample the fine summer food available at the many roadside stops. Mmmm: oden that's been heating for 9 hours! Yum!
6. Back in Tokyo and just enough time for a quick visit to one of the quaint neighbourhoods that retains Japanese character. I'd suggest areas like Ochanomizu or Nerima. Both are exciting. Don't miss the chance to see the cabbage production in Nerima - it's the Cabbage Food Bowl of the Tokyo area!
Good luck, and glad we could help! ^