The LBJ State & Historic Park is day use only no camping of any type.
There is a nice, private campground in Stonewall by the name of Peach Country RV Park if you'd prefer something very close to the park.
If you want to stay at a State Park there are several nearby, Enchanted Rock, Pedernales Falls, and Blanco. There are multiple private RV campgrounds as well in the area.
You can stay at the state park, or do what we did and stay at the Lady Bird Johnson municipal park campground. R accommodations were great, close to Fredericksburg and centrally located between LBJ and Enchanted Rock.
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