If you are going to the Shrine at Hancevill, you will really like it. Beautiful monestary, gift shop, and gardens. The nearest campground to the interstate is Rickwood Caverns, but I have never camped there. Corinth National Forest Campground is out from Huntsville, near Double Springs. It is great, but may be further than you want to drive off the interstate. Close to the interstate, but just South of Birmingham, is Oak Mountain State Park. Oak Mountain is close to the interstate and very nice, but it is South of the city in a surburb called Pellham. I don't know if this helps, but it is all I can offer at this time. Welcome to Alabama and enjoy a safe and pleasurable trip.