Check out my other reviews of the wilderness area for a general overview of the backpacking here. 

This site, in particular, is one of my favorites to stay at. It has several waterfalls nearby, is close enough to the river for easy water access, and is secluded from many other sites. It shows up in a bend in the trail after you cross over one of the small creeks. It has a large and established fire pit along with several nice cleared areas to set up your tent. Since it falls about halfway along the trail I find it is often empty and available as well. Make sure to take the short hike up the creek away from the river to see some of the beautiful waterfalls that make Sipsey so magical.