I'm a bit confused...
You write you "want to focus on the western part of Japan"..."so this time we want to go to the regions of Tohoku"?? You still haven't seen a lot in the area.
Also, when are you traveling? Especially for the Tohoku area, the season matters a lot. You mention you want to go to 4 different areas - that is too much for such a time span, unless you want to waste a lot of time rushing on trains. If you want to see Takayama, that is one good famous area. Nearby Inuyama is nice as well, and if you want to try hiking the old Nakasendo a bit, there is the Kiso Valley.
There are a number of great places in the west as you mentioned though, many largely off the beaten trail. Kotohira in Kagawa has a great shrine on a mountaintop - a trip you will never forget:
https://www.youtube.com/watch?v=ley9rVIewoQOnomichi makes a nice visit, especially the Kosanji temple:
https://www.youtube.com/watch?v=97Q5EjEOXI8You also didn't mention Nara in the Kansai area, which is a must-see city.
Farther down is Hiroshima/Miyajima, which are excellent places. Iwakuni is also a good day trip; the bridge and mountaintop castle are great:
https://www.youtube.com/watch?v=0COOZXi66mMSomeone mentioned Hagi, which is very enjoyable, and don't miss the Akiyoshido Limestone Cave in Yamaguchi as well.
If you really want to get to Yakushima, which is quite time consuming, your time in Kyushu will be limited. You might concentrate on just a few areas, like Fukuoka, Nagasaki, Kagoshima, and Kumamoto if you still have time.
For Fukuoka, see this site as a good guide:
http://www.thejapanfaq.com/fukpic.htmlThere are also many useful videos to give you a preview:
https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-0...Look into a Fukuoka Tourist City Pass also:
http://yokanavi.com/access_tourist_egOne superb sight is the Nanzoin temple, truly astonishing and totally free:
https://www.youtube.com/watch?v=lT4VQFmHFyMIn terms of history and varied points of interest, Nagasaki is the best city on the island. It is worth a couple days and Gunkanjima, while it takes 3 hours, will blow your mind.
http://www.ngs-kenkanren.com/eng/http://www.at-nagasaki.jp/foreign/english/http://www.youtube.com/watch?v=QdWRyHGW3rkBe sure to see Mt. Inasa at night if the weather is clear, and try the Nagasaki chanpon and saraudon! Also the Koshibyo temple is an often overlooked shrine that is quite unique in Japan:
https://www.youtube.com/watch?v=Mu_JnkVInTUKagoshima is great to see the live Sakurajima volcano, hiking, and hot sand baths such as on Ibusuki. Plus the Senganen garden has a superb backdrop view of the bay and the volcano. See:
http://www.kagoshima-kankou.com/for/https://www.youtube.com/watch?v=LxDmLuq6ssIhttps://www.youtube.com/watch?v=lpnDK_Wux9QIn any event, you need to think about travel time more. Look at hyperdia.com to see rail travel times, and adjust your itinerary.