Your journey into the spiritual past of Japan is soon coming to an end... but there's no need to hurry back to Fukuoka right away! The car doesn't need to be back until 7PM, so head out and explore the rest of this area, if you wish.
Alternatively, on your way back to Fukuoka you could stop off at Beppu, one of the major onsen or 'hot spring' towns in Japan. There are plenty of public baths suiting someone that wants something a little swanky, at Tanayu for example, or something very traditional, like Hoyoland.
Either way, don't forget you need to return your car to Fukuoka by 7PM!