Well, for starters, why Japan? Kinda helps us to help you if we know something of your interests.
I assume you will come in May or June. Can you confirm the date?
My best piece of advice is buy a guidebook and look at the JNTO web site. See what festivals or other major events are taking place during the time you plan to be in Japan, choose what you want to attend, and mark that on a map. From there you have a very rough outline of where you have to be at certain times.
Then, see if there are other things to see or do in those places or very nearby.
Lastly, based on whatever else you know now or read about in the guidebooks/JNTO site, choose what you might want to see. Don't forget to factor in travel time to the places. You can use Hyperdia web site to help figure out how to get there and how long it takes.
If you have specific questions about things you come up with, then come back and ask. Othewise, at this stage, it's everyone else's opinion of what you "should see and do".