you can make that loop, but you might think about choosing your arrival and departure based on best airfare to a hub city, which I sort of doubt Memphis is. Atlanta or Charlotte might be. Just a suggestion for economy.
If charlotte was your start/end, then you could go west to Ashville, Nashville, Memphis, and on returning to charlotte from Charleston (or even further up the coast). You would "miss" Atlanta perhaps. I don't think Augusta and Chattanooga would be big misses if so. I am not a huge fan of Atlanta, so I have a bias.

I share Gretchen's biases, but Memphis used to be a hub for NW so may still be for Delta, in which case the original plan will work.

This would be a great trip in the amount of time you have, and mid-October is a good time to go -- post heat, mostly post hurricane! You will miss most of the flowers -- too late for summer flowers, too early for camelias -- but otherwise, not much lacking.

Whenever possible, leave the Interstates behind for the US highways and state highways. But I am guessing that you know that.

I am going to recommend two places I have never been to but crave: Apalachicola and Cedar Key, in the armpit where Florida turns south to poke into the Gulf. Tell me how they were!

The other change I would make in your trip is to bag Atlanta and Chattanooga and go to Miami and the Florida Keys instead. They are both wonderful. Atlanta and Chattanooga are both okay.

Gretchen: Memphis was based on Virgin Australia having a tie in with Delta. As you note this may change depending on pricing when we book. I also was unsure about Atlanta.
Ackislander: Had a look at Apalachicola and Cedar Key both look great, may have a re think on route. No sure about Miami though.
Thanks for your input...

That's good for you.
If you decide to not do the Augusta- Atlanta on your loop, I could suggest coming up through NC, maybe even including Winston Salem (and see Old Salem there--a restored historic site), and then on to Asheville for Biltmore House.

What are you wanting to see and do?

Your initial plan is to go EAST along the Gulf Coast (New Orleans to Florida), not west. Given the time of year you'll be here, consider the most culturally immersive experience possible: attending an SEC football game. You'll be smack in the middle of conference play. None of the SEC schools are on or near the Gulf or the Ocean except UF.

Note that Asheville is said to be very nice (only driven through or around it myself) and North Carolina generally is too.

A full circle isn't necessary unless your path requires it - Memphis was a NW hub and will connect with whatever Delta flight you take from OZ to LA, and Atlanta is THE Delta hub so starting at one and ending at the other could work. I'd also minimize time in Atlanta - has an a------ factor close to Boston's, which is pretty shocking for the South.

BigRuss: the SEC game is something I would like to do. Who's home games provide the best spectacle?
Also not sure what you meant by "an a----- factor"
Thanks

The best spectacle for an SEC game would probably be one of

University of Alabama (Tuscaloosa)
University of Florida (Gainesville)
University of Georgia (Athens)
Louisiana State University (Baton Rouge)
University of Tennessee (Knoxville)

University of South Carolina (Columbia) might fit in there, too, but not quite at the same level?

The other SEC schools are either not as spectacular (U of Mississippi, Mississippi State U, Vanderbilt U) or not along your potential route.

Also, tickets will probably be pretty hard to get (less so at the 3 "second-tier" schools I cited) and expensive even if you do find them.

You have to factor in the opponent as well, of course. There will still be plenty of atmosphere if the opponent is weak, but (usually) not as much drama on the playing field. And a weak opponent might mean more tickets are available. Homecoming is another thing to factor in (special events honoring alumni, such as 25- and 50-year anniversary classes).

Not SEC But, OU/Texas combined with the State Fair is about as All American as it gets.

You have plenty of time for the great trip you have planned. Consider including Asheville, North Carolina, The Great Smokey Mountains, Miami Beach, the Everglades, Corkscrew Swamp, and the west coast of Florida before driving east to New Orleans along the Gulf.

HTtY

An SEC game would definitely be a cultural experience. Of Cranachin's list, Alabama would be hardest to get tickets for (they just won the national championship... again; as I'm sure a Bama fan would point out if I didn't, they've won three of the last four). Tennessee has done the worst of that list for the last few seasons (much to my disappointment, as a native Knoxvillian!), so crowds might be less enthusiastic, but the spectacle will still be there in full force and it would be easier to get tickets. Also, ticket scalping is legal in Tennessee, and you would likely be able to buy tickets on the street the day of the game.

The University of Mississippi (aka "Ole Miss") is more known for their pregame tailgating and see-and-be-seen atmosphere than for their football prowess, but it'd be fun too. Vanderbilt (Nashville) doesn't have the atmosphere or tradition of many of the other SEC programs, but they've done really well the last couple of seasons and people are fired up about them, so if they're still doing well next season that could be fun. I'd plan your route, take a look at the home schedules, and see what you can fit in.

"a------ factor" - Russ meant that people in Atlanta have the reputation of being not so nice, especially in comparison with the rest of the South, which is known for friendliness and hospitality. That's a complete generalization, of course - Atlanta has some lovely people - but in general, Atlanta is a big, sprawling city with crazy traffic. There's some fun stuff to do there if you end up flying in or out of it, and probably the best shopping in the South, but personally I try to avoid it. To each his own, though.