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Even at a relatively relaxed pace, it would only take three days each way between New York and New Orleans, leaving you eight days or so to explore things on the way and enjoy the Crescent City. As is my wont in such cases, I will suggest simply that you take two completely different routes down and back, say the Blue Ridge Parkway, I-81, I-75, I-59 down with possible stops in Blacksburg VA and Tuscaloosa AL (college towns) and Gatlinburg TN (gateway to Smoky Mountains National Park) among other possibilities. Then on the way back you can take the Natchez Trace Parkway up to Nashville (great Country and Western music scene), then I-65 up past Mammoth Cave National Park to I-64/I-79 through the central Appalachians. Whether or not to include Philadelphia, Baltimore, and/or Washington is entirely up to you as you can easily bypass them entirely or head right through them in either direction.

AZBuck