Charleston has Fort Sumter and Patriots Point Maritime Museum with 3 WW2 vessles, the USS Yorktown, the USS Laffey and the USS Clamagore. Town has the historic market district and the historic homes and lots of great dining. Think about stopping in Savannah before you head to Charleston.
Then head on up to Asheville and go to the Biltmore Estate. Plan for all day there if you go. Take one of the add on tours like the roof top tour or the grounds tour. Look online at the options. Eat at any of their restaurants they're all execellent. The Asheville area is worth about 4 day stop to explore.
Then come over to Sevierville, Pigeon Forge and Gatlinburg. Yes, its "touristy" but there is lots to see and do. Depending the time of season you hit here you might see very heavy traffic and patience would be in order. Great dinner shows and Dollywood is a great theme park (they say they are NOT an amusement park!). Again there are lots of other great restaurants and there is the Great Smoky Mountain National Park with Newfound Gap and Clingmans Dome and Cades Cove. You could spend another 4-5 days here. I live in this area and can answer most questions you might have.
From there head west to Nashville and take in Broadway street with all the little honky tonks and live country music. The not to be missed is the Hermitage, Andrew Jacksons home and museum. From there Memphis might be a stop for Beal Street.