Tldr: A 4wd dirt road out to the canyon with primitive (open dirt) campsites and a few fire rings.
The sheeps bridge road that gets out through the campsites has camping options from right off the highways to deep into the fields by the virgin river canyon. All are primitive, and many have fire rings. I did see some RVs near the highway, but no hookups or dump sites. A number of hiking and off roading shortcuts can get you in and around the area. While there are no large rocks to worry about, after the first couple miles its best to have a four wheel drive high clearance vehicle, as the roads get rutted and in rain very muddy. I made it around easily in a Mitsubishi outlander sport with 4wd. Many campsites are clearly visible by the signage as well as visible fire rings. The fire rings have spikes and mounts for convenience. Due to the elevation and canyon, this area is slightly warmer in the winter, and was not snowed over when the rest of zion was, so it made for good camping (the ground was still frozen). My friend and I had no trouble staking down, and the local gas stations (less than 30 min drive in any direction) all had firewood in the winter. We drove and hiked into the canyon easily from the campsite. Overall a fantastic primitive campsite for good canyon access, nearby hikes, and a few non sandstone climbs/boulders during rainy seasons.
The main trail is composed of a gravel camping road that encircles the man made lake. The road is bike and vehicle friendly, though it seems only park vehicles are allowed. Several trails offshoot from this main road, each is marked for either hiking (trail running), mountain biking, or camping. Theres several large camping sites, and both the bike and hike routes seem to be loops that end back at the starting offshoot on the main road. None of the hikes are very difficult, most are easy/moderate and support running. They are very easy for hiking. Some bike routes are more difficult. Half are in woods with trees as low as 5ft over the trail, the other half go through open fields. Since there are many different routes to take, its easy to increase or decrease the distance. I had no trouble clearing four miles by running out, doing a trail (full loop) and running back. The loops aren't always possible to cut, so keep in mind that its sometimes hard to tell how far along a loop you are. Note that few of these trails have views of the lake; only the campgrounds, bench sites, and main trail/road are unobstructed to the water. There are several beautiful views of the small damn and the broken sections that create a little waterfall. The sunset in particular was really peaceful and easy to watch from the benches (perfect for a romantic picnic).