Lewis - I believe it is called the Waipio River (pronnounced "Y-P-O"). It runs through the Waipio Valley on the big island of Hawaii. It's a real isolated valley that can only be reached by hiking or via a steep road that requires 4 wheel drive:

http://www.hawaiihighways.com/photos-Waipio-Valley.htm

http://www.uwec.edu/jolhm/hawaii2005/day4/waipio/waipio_valley_map.htm

We signed up for a tour when they drove a group of us in and then mounted us on horseback to ride around the valley. It was really wonderful (and yes, we had to spent extra movement points to mount and dismount).

It was a great day. We spent the morning at Hapuna beach and then drove to Waipio for the ride. It was a great way to see the valley which is absolutely stunning to be in. They gave me the largest horse in the stable. It was one of the high points of our trip.