Location: off the 58 in Onna, if driving north on the 58 take a right at the light just before the Renaissance resort (ie before you get to Malibu beach; the resort is not in sight at the correct intersection). There is a concrete ramp going off to the left, also a dirt track; either one takes you somewhere interesting. The area is marked with blue and white signs in Japanese which point to caves, etc.
This area leads to the terminus of a mountain bike / hiking trail called "the luge" by bike enthusiasts. In order to get to the top of the trail, you first go to a lookout point with views over Onna and Ishikawa (the narrowest part of the island). To get to the lookout, take the 6 towards Bios on the Hill / the Royal Garden resort and golf club, and turn at the huge sign indicating the way to those landmarks. Keep driving until the lookout tower is visible. There is a small parking area and stairs lined by sakura trees lead to the tower. Behind the tower a trailhead is visible. When we went, someone had left pornographic pictures lying around here, so watch out if you have kids along. This trail is "the luge" and is a little over a kilometer long. Down the trail a couple hundred meters another trail comes off to the right, this leads back to the driveway / parking area just downhill from the lookout entrance.
There is also an alternative start to the Yamada stone bridge path. This is just off the 58 north of the Ramada. Take the right just before the big Nakadomari souvenir / food shopping area, there is ample parking and a sign with a map of the trails. If you miss the turn don't worry, just take the next right into the shopping area and double back.
This is a great area for hiking. Tons of different trails lead to caves, many of which are dedicated as Shinto shrines. The trail to the stone bridge appears to be a traditional rural highway, some of it paved in cobblestone. The trail called "the luge" heads south-southeast for quite some way, passing through some lovely wooded areas. Side trails lead off to the creek, caves, whatever.
The area gets pretty muddy. Torches, rope, and old clothes serve you well in the caves. Bring a bento box and some water and many pleasant hours can be spent exploring.