If you rearrange things, you could probably use a 14 day pass and make it work. Going to Yokohama is peanuts. For Nikko, you can use the Nikko Pass, and for the Fuji area, use the Fuji Hakone Pass.
It's unclear what you're going to Nagoya for. Every place has something, but it's one of the least interesting places. Even my taxi driver there was dissing the city to me. That said, Meiji Mura in Inuyama is absolutely marvelous.
For Shirakawago, I hope you're aware that there is no rail access there. You have to pay for the bus.
As for "not very interested in Hiroshima" I take it you are referring to the Peace Park/Museum, as if that were the only thing in the city - many people have that misconception. There is far more to explore beyond that if you are willing to look. The Shukkeien Garden is really beautiful, plus there is the "secret" jewel of the city - the Mitakidera Temple - which is simply stunning and completely unknown to most.
https://goo.gl/fAz4axBeyond the city, there is also Miyajima, plus Iwakuni is absolutely delightful.
https://youtu.be/0COOZXi66mMOkunoshima (Bunny Island) though was all but not worth the time and trouble to get to. The rabbits are cute, but nothing like some travel videos hype the place. Some bring carrots or cabbage to feed them, but they seem to like the rabbit food a lot more (small bags on sale at the ferry office).
You have more than 7 days set for Tokyo - but 3-4 days may be enough unless you have a long list of places you're dying to see.
https://is.gd/D3QTIRThere are some other day trips you could take in addition to what you have - Kusatsu, Karuizawa, Nokogiriyama, Kamakura/Enoshima, the Ushiku Great Buddha, Takao, Okutama, and many others.
No visit to Japan is really complete without going to a hot spring at least once.