Loved this gorgeous and secluded area! There are, in fact, a few designated campsites along the road. Most of the area is day use.
I was nervous about trusting Google to get us to the right spot, but this map location is quite accurate. The drive getting there was absolutely beautiful, and the hiking itself was just wonderful. Important (maybe) to note that there are two trails, and you make a choice once you get to the bridge pretty early on:
(1) Crossing the bridge will take you to a trail that pretty quickly becomes switch-backs up the mountain. Becomes quite strenuous and narrow with some slippery rock areas. We made it up to the big rock with the cave (note that you’re not supposed to enter the cave gate to respect the bats). Very worth the climb if you’re able — our 4 1/2 year old made it with some help along the way.
(2) The 2nd trail seems to follow the river through the canyon and would be less difficult. I followed it a ways just to check it out, since by then my young son was quite tired. So, maybe another reviewer (or trail map if it exists?) can confirm my impression of a more flat and lovely trail with pretty constant rover views.