Head upward on the rocky doubletrack from the gravel trail near the bridge and ruins. There are two singletrack trails. Both trails head in the same direction, but the higher trail is longer and more fun.
This trail is fun and a pure natural singletrack with a variety of obstacles. The main South Park Trail is in a fenced-in area. There are two gates that are along a gravel road that you'll cross. One gate is up at the top of the hill and one is down near the river. You can go either direction on this trail.
Go through the gates and make sure you close them. There are some side trails off of this but they are all short connectors and you eventually will make it back to one of the gates.