There are many facets to Japan - if you don't like big cities, that is fine. Southern Honshu, Shikoku, and Kyushu offer a wealth of good places that are not overrun by the tourists.
Miyama north of Kyoto is very quiet and tranquil, with a taste of old Japan. If you want to go deeper into things like this, try Shirakawago & Takayama.
Okayama is not far from Osaka and it is famous for its castle, plus Korakuen Garden
https://www.youtube.com/watch?v=5zAI3_N7NEM which is one of Japan's Top 3, and also the Handayama Garden is beautiful:
https://www.youtube.com/watch?v=JGQ8o7k9GbA The half day hike up to Konpirasan in Kotohira, Kagawa
is stunning.
https://www.youtube.com/watch?v=ley9rVIewoQGoing to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
https://www.youtube.com/watch?v=afx-Ju52FiYHiroshima also has a number of good places. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular.
https://www.youtube.com/watch?v=97Q5EjEOXI8Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain.
https://www.youtube.com/watch?v=0COOZXi66mMAnd if you really want something mind blowing, go see the Akiyoshido Limestone Cave in Yamaguchi - a 300 million year old marvel with an underground river going through.
https://www.youtube.com/watch?v=DqIKC9S8TFQHagi is also a joy with old time flavour.
https://www.youtube.com/watch?v=wjw577xBinIFor Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a detailed guide:
http://www.thejapanfaq.com/fukpic.html Don't miss the Nanzoin Temple which is one of Japan's finest yet, almost totally unknown to the tourist book "experts" and completely
free!https://www.youtube.com/watch?v=lT4VQFmHFyMLook into a Fukuoka Tourist City Pass also:
http://goo.gl/XFQSweYou can also see a lot of previews on the best there is to see at
https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-0...In terms of history and varied points of interest, Nagasaki is really the most interesting city on the island.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-gbw2yXNLK92siHyNqSNx...Gunkanjima is simply unforgettable.
You should have plenty to see and do with all that.