There are several campsites at Dominguez, which are often rather taken, especially earlier in the season...most people stop and park at the mouth and then walk down to see what's available. There are some commercial canoe groups on the river, which go for the official "large group campsites" if they can - though getting later in the season so won't be as much competition. The 3 larger spots are at the mouth, about halfway down the left channel, and the farthest downstream. You can hike a large trail to see which are taken (there's a sign in at Escalante, but not all people end up properly signing in, plus you don't know who has hiked in from the pedestrian bridge, so there are no guarantees of sites). If you're a single raft (or even a couple), there's also a smaller campsite just below what we call "Lizard Rock", between the first two big campsites.
Also a campsite river left for a medium sized group in the last left-hand turn before Dominguez, and then on around where the train tunnel happens river right several miles below Dominguez (and below Bridgeport).