Itinerary ideas?

Hi,
You may have to rearrange the order of some things, but it is easily doable.
It's not clear why you'd give the Kiso Valley 2 nights - one is quite enough, but if you want to see the area more, you could spend some time in Matsumoto, or Karuizawa. You could even go to Kansai by way of Kanazawa, which also is an excellent city to explore.
Since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5 PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are superb.

If you wanted to add more time down south, that is possible too. Just beyond Miyajima also lies Iwakuni with its historical bridge and mountaintop castle. Taikodani is also a beautiful shrine in Tsuwano, Shimane. One of the very best places nearby is the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it.
Closer to Kansai, Okayama is not far and it is famous for its castle, plus Korakuen Garden, one of Japan's Top 3, and also the Handayama Garden. If you'd like to get off the beaten trail for a while, the half day hike up to Konpirasan in Kotohira is stunning. Going to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
Closer to Tokyo there are many good places too, including Izu, Kusatsu, Takao, Okutama, the Fuji 5 Lakes, and Hitachi Seaside Park.

There is no shortage of good places.

Two extra days are still not enough!

Hi there, I too am going to be doing 14 days in Japan - leaving in two weeks, very excited! My itinerary is quite similar to yours, except that I have added an extra day to visit Naoshima - also known as "Art Island". Some friends have told me it was their favourite part of their whole trip in Japan, so if you like art, that might be an idea? I will be going to Naoshima from Hiroshima, you take the JR train from Hiroshima to Okayama (1.15hrs), then Okayama to Uno (1hr), then a 20min ferry to Naoshima from Uno. I am staying the night in Naoshima but you dont have to do that, you could stay the night in Okayama as Toraneko above has also suggested.

Either way I am sure you are going to have a great time!