Hinokage (map) has a tiny population of just over 4,000 people, and is very well known for its three massive bridges, each spanning picturesque emerald chasms, and for its traditional Kagura dances. It is also known as the origin of Kazuo Hiroshima, a famed bamboo basket weaver. Despite its declining population, it remains part of the northwestern quad of notable towns (Hinokage, Takachiho, Morotsuka and Gokase). This region has also been classified as a world agricultural heritage.
Hinokage has a free Wi-fi service for tourists, as well. For more information, check out their page here (Japanese only).
City Website: http://www.hinokage.jp/