A popular walking route is the 11 mile circular Highmeadow trail. Taking in stunning views, caves and plenty of woodland, this is a great but slightly challenging trail. It also makes for a great trail run. You can start the walk from King Arthurs cave, only 5-10 minutes walk from the campsite, the route will then take you over the bridge, up to Staunton and round to Yat Rock viewpoint before descending back to the river where you can either take the hand ferry or add a couple of miles on by using the suspension bridge.
You can find a detailed description of the route here.