Hike near Kamikochi or bike Shimanami Kaido

Looking for opinions on end June 2015 with 3 extra days. Husband, Daughter (10 yrs) and I have 3 days to plan in Japan. We are wanting active days and to see natural beauty of Japan. We will be in Tokyo before and after and later plan 4 days near Kyoto. Want to be in quieter spot for few days.

Anyone recommend hiking in Japan Alps in or around Kamikochi or Nagano OR we have been thinking of the bike tour Shimanami Kaido for 2 days.

Open to other ideas - even considering Kiso Valley hike or Hakone.

Daughter is active and good hiker/biker so not worried about her keeping up.

Kamikouchi is great though there are hordes of tourists arriving by bus and you can lose a bit of the peace. But we got quite attached to the monkeys in our 3 days there (my wife had previously thought them to be pretty disgusting, but they are much more interesting in the wild). Less so the relatively large striped snake that slithered across our path, that was a surprise. Saying overnight is really nice, you get the place to yourself - we stayed at the Onsen Hotel which is just brilliant.

I didn't think that the Kiso Valley was as interesting as I hoped it would be. Maybe my expectations were too high. If you don't expect much, it will probably be awesome.

Other places to consider that are easy are Takayama (some nice bushwalks around the park which is harder work than you'd think, also the town is great, and the squirrel park just out of town is amazing for those of us who aren't used to squirrels), also close to Shirakawa that has some nice scenery.

I'd also throw in Karuizawa. That is a great place, underrated I think. It has a great hike from the top of the shopping street to a lookout a few km away.