The whole premise of your first question is mistaken. Yamaguchi has some very good sights.
Just across the straight from Kitakyushu is Shimonoseki, which has some good places to visit, though as anywhere it depends on your interests.
Plus, the Akiyoshido Cave is the most impressive limestone cave in the whole country, and there are over 100 in Japan. There is no other places to walk through huge caverns over 300 million years old with an underground river rushing past you - it is simply stunning.
https://youtu.be/DqIKC9S8TFQThe Akiyoshidai plateau above also offers some good hiking trails through was was the bottom of the ocean and a giant coral reef hundreds of millions of years ago. In Nagato, there is also the Motonosumi Inari Shrine, one of the best in Japan, yet totally off the radar and unknown to all the tourist guidebook "experts". Likewise to the east there are the "Sea Alps", a really picturesque rugged coast with some nice hiking. The problem though is that it is very painful to reach if you are not driving.
You mentioned Hagi which has its charms too.
Iwakuni has the nation's loveliest old bridge and nice mountaintop castle.
https://youtu.be/0COOZXi66mMYamaguchi City has some good temples and shrines already mentioned on this site. There is also in Shunan City the Kanyoji Temple which has a number of amazing traditional rock gardens - normally I don't really care about karesansui type gardens, but this place is really head turning.
There is also Tsuwano in Shimane which has some historical places too.
You already mentioned Hiroshima, which also has quite a lot - far, far more than just the Peace Park, which so many day trippers go see and then leave the city for Miyajima.
https://goo.gl/fAz4axIf you are going in September, then if you can make it over to the Sera Kogen Farm you'll be just in time for their annual dahlia festival - something you have to see to believe.
https://sera.ne.jp/en/dahlia/
There is also Sandankyo Gorge, just 75 minutes by bus from Hiroshima Stn.
http://visithiroshima.net/plan_your_trip/tour_plans/sandankyo.htmlAs for the rail pass, you can buy it in Japan now, but it is about 15% more expensive. I can't think of any ordinary reason to hold back and wait til you're in Japan to get it - if you go to Japan without knowing where you're going, you are doing things seriously wrong. But for very long trips like yours, a rail pass often doesn't pay off because you are not traveling that far quickly enough. A series of regional passes might work better for you, or just regular fare tickets.
https://www.japan-guide.com/e/e2357.htmlIn short, just because you don't hear anything about somewhere doesn't mean there is nothing there. Sometimes you have to start digging, and you can often find some extraordinary places to see.
