What to visit between Fukuoka and Hiroshima

We would like (my wife and me) will travel from Fukuoka and Hiroshima. What can you advise to in West Honshu. Despite the fact we have 4 weeks for holiday in Japan we just can afford max 2 days in that area. Are there really sights and hikes worth to visit that area?
Thanks in advance,

my vote is for Hagi
http://www.japan-guide.com/e/e6150.html

Between Fukuoka and Hiroshima (assuming Iwakuni is included with Hiroshima) there are plenty of options on 2nd tier cities such as Mojiko, Shimonoseki, Hofu, and Yamaguchi. Shimonoseki is a must see in my book, which is the most famous place in Japan for fugu, or blowfish. The big fishmarket there has no peer when it comes to the sheer variety of negiri sushi. Plus there is a big aquarium, a nice seaport/boardwalk area, and a samurai area of town. You can rent bikes to navigate:

http://www.city.shimonoseki.yamaguchi.jp/seisaku/kokusai/gaikoku/sight...

http://www.city.shimonoseki.yamaguchi.jp/seisaku/kokusai/gaikoku/meal/...

http://www.travel-around-japan.com/k73-06-shimonoseki.html

For an extended trip, take the footpath under the Kanmon Strait to Mojiko (yes, it's underwater). Here, a bike comes in handy. Fugu dishes are cheaper in Mojiko.

There are some interesting spots in Yamaguchi Prefecture such as the Akiyoshi Cave, Hagi, Iwakuni (with a castle and a famous bridge) and Shimonoseki from where you can walk over a bridge to get to Fukuoka. ;)

You can also visit Tsuwano (castle ruins and a huge Inari shrine).

I can third Hagi. Yes it's a bit out of the way (normally a bus from Yamaguchi), but it's a fantastic place which is less unspoilt due to being so far off the Shinkansen tracks. I travelled around Chugoku in December/Jan, so going to my main page and looking at the user reports might give you some ideas.

For hiking, Akiyoshidai is probably the best place. First you can walk through Akiyoshido Cave, which is very impressive, and then you can walk along the many trails through the karst landscape of Akiyoshidai Plateau:
http://www.japan-guide.com/e/e6130.html

Biking is quite nice in Yamaguchi Prefecture.

Yamaguchi City is great to navigate by bike:
http://www.japan-guide.com/e/e6100.html

Also, Hagi, which others mentioned is a good place for biking:
http://www.japan-guide.com/e/e6150.html

Hofu is another nice biking town:
http://www.city.hofu.yamaguchi.jp/site/kankou-site/hayawakari-english....

All of those that I listed as nice for biking can also be made into walking courses, too, if you prefer walking/hiking.

I also like Yanai and its historic town:
http://members.virtualtourist.com/m/a40e1/ec63b/