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New Orleans would make a fine destination city for a week-long Road Trip out of Orlando. But note that the direct route between the two cities basically just follows the Gulf Coast (more beaches) and because that coast is a tourist destination in its own right and houses a number of military bases, you won't get much of a feel for what makes the South unique. So, I'd suggest that you look at a more inland route and plan on taking a full two days each way, which would still leave you four days or so in the New Orleans area.
One possible inland route would be I-75 up to Valdosta GA, then US-84 west to Laurel MS and I-59 (or US-11) down to New Orleans. That adds about 110 miles and a couple of hours to the drive, but it will give you a better look at 'The South' and you aren't going to complete the drive to New Orleans in a single day anyway. Along the way, you might want to check out Okefenokee Swamp in south Georgia (a bit off the route), the United States Army Aviation Museum, Frank Jackson State Park, Choctaw National Wildlife Refuge, De Soto National Forest, or Paul Johnson State Park.
In the New Orleans area, a day trip either west to the Creole Nature Trail or south along the Mississippi Delta would also be in order as would (perhaps) a drive across the Lake Pontchartrain Causeway.
AZBuck