You don't mention when you will be in the area so be forewarned, the Fredericksburg area can be very busy especially on weekends. Lot's of places to camp, the question will be can you get a reservation when you want. I will throw out Pedernales State Park as an option near Johnson City. Again, if you can get a reservation.
FrankoToo
2018 Cruiser Stryker ST2313
2011 Ford F450 6.7L PS 4X4 Crew Cab Lariat