We just took that trip. You'll have a ball. Kartchner Caverns State Park near Tombstone Az is a place we really enjoyed. Fort Stockton, Tx is almost a must overnight spot and we like the Fort Stockton RV Park (it used to be a KOA and has an on-site cafe called the Road Runner). Buckhorn Lake Resort in Kerrville, Tx is very nice but pricey. We stayed near downtown San Antonio at a place I think was called the "Traveller". It was cool because the bus stopped right in front and would take you downtown easily.
In New Orleans, we actually stayed right in the French Quarter at the French Quarter RV Resort. It's expensive (~$70) but you can walk to Bourbon St... walking back can be the hard part!
In Fla, near Titusville we stayed at the Great Outdoors which is remarkable. On the way we really enjoyed southern Alabama near Mobile. We belong to Escapees and got to enjoy their great parks both there and in Bushnell, Fla for only $85/week.
You got some great advice. Pick a few things you want/must do and make those the cornerstone of your trip and let the rest flow... and take time to relax too. We full time now and the Shuttle launch on 4/5 was one of those cornerstones for us.
Have fun and travel safely...