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I'm not from the Shreveport area, but have camped a couple of places that are a few hours from you. Chicot State Park in Ville Platte is about 2½ hours from Shreveport and is a quiet, hilly, wooded campground. If you have children or prefer the "party" atmosphere, Cajun Palms RV Resort in Henderson (just outside of Lafayette) is about 3 hours away from you. They have a water park that is included in your stay. It has everything from a water playground, to water slides, to a bar all in the different pools. The best part is there is no additional fee to use the water park, and the rates are very reasonable IMHO. $40/night ($36 with Good Sam). Good luck in your travels.
2013 Voltage Epic 3600
2006 GMC Sierra 2500HD Diesel (LBZ)