7 days to see the real Japan with kids

We will be going for 7 days in mid-April and want our kids (8 and 11) to experience the "real" (traditional) Japan. No Tokyo Disneyland and KFC but ryokans, onsen and sashimi (and hopefully some cherryblossem). We want to do a railpass and visit 2 or 3 different places. Does anyone have recommendations for some nice and accessible ryokans in the country where kids are welcome?

Kyoto
Takayama
Shirakawago
Mount Koya
Kiso Valley

are some suggestions for seeing the "real" traditional Japan:
http://www.japan-guide.com/e/e623a.html

Eric, you didn't say where you will go! Tohoku, Kanto, Kansai,Kyushu?
please don't shortchange modern Japan! the elevated freeways, covered pedestrian streets, huge ferris wheels, very fast trains, etc. are the real Japan too!
with only 7 days I would only tour the Kansai (the birthplace of Japanese civilisation)with Kyoto, Nara, Kobe, and of course Osaka, all 30-40 minutes from one another by commuters trains.
most Ryokans, at least from the medium priced ones and up have rooms for 4, with tatamis and futons on the floor.

My recommendation, made without knowing you or your kids, so take it with a grain of salt, is to break up the trip- as far as accommodation goes - so as not to go overboard on the ryokan side of things. Maybe that was already your intention. My husband and I have made several two- and three- night trips to the 'real Japan' and it ends up being kind of...suffocating. A small traditional ryokan is a fairly strict place as far as their routine, what options there are for food, etc. Ryokan hotels offer more freedom as far as noise-proofing, larger baths, bigger public spaces (lobby, often a game room or karaoke), less individual attention (that can be GOOD thing) while still offering tatami mats & futons, Japanese food, and Japanese customs. www.japaneseguesthouses.com is a good resource; even if you don't use their service, their write-ups on various ryokans is very good.
Mid-April is festival time in Takayama, so accommodations will be hard to get. Last year, when we went to the spring festival, it was just a bit too early for cherry blossoms.
Matsumoto has an original castle and nearby onsen towns of Utsukushigahara and Asama have many ryokans and hotels. Though there too I think it may be early for cherry blossoms.
In the Hakone area you can experience Japanese ryokans/hotels while within reach of many activities - and, if you are lucky, a good view of Mt. Fuji.