I second inuyama, as for Ise ... it's usually very crowded and the places itself are quite "plain" ... that place has a great spiritual importance, but isn't the most stunning visual experience to be had.
There are some more:
Kanazawa is very nice and there is a new Shinkansen going there since only 2month or so. Has an old Samurai district, some Geisha districts and one of the 3 famous gardens in Japan.
I'm very fond of Takamatsu, which has in my opinion the most beautiful garden in Japan and some village were they moved traditional buildings from all over Japan. Can be used as base for exploring some more of Shikoku or Okayama which is on the way and host another of the 3 famous gardens.
The third famous garden (Kairakuen) is in Mita, only 100km from Tokyo. I have never been there an it's famous from plum blossom ... so probably you are a bit late
Takayama is a very nice and different town, as it used to be a merchant town. Lot's of historical buildings, but more merchant buildings instead of the usual shrines and temples. the also have a famous festival 2 times a year and you can atleast visit a museum to look at the shrines they carry around. The local food and the local sake breweries are great too. If you take the train from Nagoya, thats a special scenic train that even has some anouncements on the way.
Koya-san (Wakayama-ken) is the city of 100 temples or so, I think there is no hotel in the place, but you can stay at a temple and participate in the ceremonies. Very peaceful place, but you can see everything in one day.
Yamadera in Yamagata-ken is also great, atleast in autumn, probably not as colorful now, but great mountain scenery.
Matsushima - havent been there, but on my to do list, one of the 3 famous scenic spots of Japan
Kyushuu is worth a visit, Hakata/Fukuoka is ~6h if you can use Nozomi. You can stop at Himeji on the way. On Kyushuu Kumamoto with it's famous castle (I think the biggest in Japan) and Kagoshima and Beppu are definitely woth a visit, if you like nature, you may also want to go to Mt. Aso (the train ride from Kumamoto again is a scenic one). If you like Onsen, Yufuin and Kurokawa are worth a visit (yufuin I think has a train station, kurokawa-onsen is a bus ride). You also have Nagasaki. Fukuoka is quite convenient as base (with a rail pass), as you can reach all the above mentioned within 1h or 1.5h.
Things on the way:
Nara near Kyoto is worth a day
Uji near Kyoto with byoudoin is something you can do on your way
Himeji hosts Japan's most famous castle and is directly on Shinkansen line between Osaka and Hiroshima
Okayama hosting one of the 3 gardens is also on said Shinkansen line
Miyajima is I think ~1h from Hiroshima by bus&ferry and worth atleast half a day, if it's not on your planned tour, you could do that on the way back from Kyushuu
Hope there is something for you in between. Depending on your time allocated for Kyoto, you may also consider doing something in Kyoto that is not on your list. Kyoto area can easily fill one week.