Given that you will be there from Thursday - Saturday, and that we are in October now, I think camping at the beach at the S Turn would be a good bet. You can get there two different ways.
A. You could park your car at the Parker access, wade across the river (knee deep) and follow the trail upstream. You will come to a spot where the river is in plain view and across the river from that spot is a large beach area. It's less than knee deep to cross over to that beach there. Going this way would be just over a half mile hike. And going this way there are a few other spots that you might decide are more fitting to you, but the S Turn area has a large beach area.
B. This route would get you to the same spot without having to cross the river, but it's much longer, you can get lost if you don't know the route (it's not marked at all), or at least leave you wondering if you are going the right way. It would also require you finding a place to park your car other than Parker access, as it would be even longer. For instance, if you had to park your car at Parker access, the total hike distance would be close to 4 miles.
If neither of those appeal to you, I can give you a few more ideas...
Here's the hike from plan A from above:
If you need directions on how to get to Parker let us know.