Dazaifu Temple （大宰府）
A very big and cool temple in Fukuoka prefecture. There is also a traditional style Japanese street lined with traditional looking Japanese shops. Definitely go.
Google coordinates: 33.521147,130.534079
Aso Shrine (阿蘇神社)
This is a nice shrine in Aso city. If you go to Aso you should check it out. There is also a neat little traditional style shopping street nearby. The street is line with natural springs, so great for getting hydrated.
Google coordinates: 32.948218,131.115432
A huge temple complex in the mountain. Really cool!
Google coordinates: 33.150846,130.52526