We have enjoyed staying at Askew's Landing near Edwards, MS several times. It would not be everyone's cup of tea: simple, quiet, rural setting with lake. When we were there no concrete (or asphalt) pads.
We have also stayed in Vicksburg at the Ameristar Casino campground--almost exactly the opposite setting, and at the Magnolia RV park.
On the other side of Jackson is Roosevelt State Park where we often stay.
Yes, there are some rough spots on I-20, but we have survived them many times.
Be sure to take the south loop (I-459) around Birmingham. We've never even had to slow down. We have enjoyed Tannahill State Park which is not far off I-459.
As for Atlanta--that depends on where you are going in the city. Our destination was usually Stone Mountain RV Park, so we went straight through on I-20 to the infamous loop 285. I can see where it gets its reputation, but we always made it fine by staying off the right hand lane until we were near our exit, sticking to our lane, and driving at highway speed--most will pass but that's ok.