I have worked in Japan (2 yrs) as a mechanical engineer, and my wife and I have viseted on a couple of 2 week vacationes and we had a BLAST. We have also hosted students (homestay) from a particular private highschool, and we've gotten a chance to visit the school and the students sometimes, too!
Japan can be awesome and frustrating at the same time. So - first question: How much Japanese do you know?
This will determine how far off the beaten path you can explore, seeing and doing things YOU find significant, rather than a canned tour-bus full of mundane Americans.
Next: What do you KNOW (in advance!) about the places you want to visit? Nothing is quite the bummer than spending thousands of dollars to go here-n-there, then you get back home and find out that there was a cool shop/store/museum/ traditional thingie or important landmark RIGHT NEXT TO the hotel or ryokan you stayed at! (And I missed it, dammit!!!) Google can be your friend in helping you find out all the stuff about the points of interest you are thinking of hitting.
Three: Can you handle a ryokan as opposed to a hotel? This relates to your language skills (above) but also whether you can enjoy traditional Japanese accommodations (the small, high-density bean chaff pillows*) and traditional foods such as grilled salmon, eel, or river fish for breakfast, natto with raw egg (yum! - for me... YMMV...) miso soup and green tea. If you enjoy typical traditional Japanese fare, ryokans are usually much less expensive than Western-style hotels, and include breakfast or dinner (and sometimes both.) It's kind of impolite to blow off these meals even if there is a kick-ass restauraunt you want to hit - do that over LUNCH. If it's a small, family-run enterprise they will quietly feel bad if you don't accept the food they prepare - it's often already included in your bill, so it's like paying them for doing nothing and then you grab an an-pan at the am/pm or Lawson convenience store down by the train station... The family will take it as: Really? We can't cook any better than that...?
*DO NOT do pillow fights with those, they are like cannon balls and you will sprain someone's NECK. (This is why in an anime pillow fight at a school summer trip, the characters get seriously decked by these things.)
But you can save some ¥ ¥ ¥/$$$ by staying at ryokans...
Four: Are there any festivals happening during your time there, or do you want to time your vacation to hit special events such as onbashira or yabusame, or certain temple rites, harvet times, etc?