On your way over to Gaitlinburg, make sure you stop in Asheville, NC. The Biltmore estate is there, which is a fantastic stop. You can then drive through Smokey Mountain National Park to reach Gaitlinburg. Leave yourself enough time to pull over on the side of the road a couple of times and explore the scenery
Thanks - we ended up stopping at the U.S. Space & Rocket Center in Huntsville, It was a quick side trip off the main route and we all really enjoyed it. My youngest is even doing a report on the US Space program he enjoyed it so much.
We were able to visit St Augestine and take the trolley tour and had a great time. I love archtiecture so it was a special treat for me. I will be recommending St Augestines to others for now on!
Have you ever checked out Chattanooga? It's a great small city with some beautiful architecture, interestig cultural stuff happening, and history museums, zoos, festivals, etc. There's some basic stuff here: https://www.tripadvisor.com/Attractions-g54946-Activities-Chattanooga_Tennessee.html
Also there's some really great food!
Atlanta, Georgia is a lot of fun. And very close to where they film The Walking Dead if you're interested in that. There is a cute little town near the film set. Also, Athens is a great town.
I would really recommend Savanah, Ga. It is probably the most beautiful city in the US in my opinion and certainly has it's share of history!
If you leave Destin and head east you can go up to Savannah, Georgia and then up to Charleston, SC. Those are some of the prettier places north of Florida and not too far out of the way. Charleston definitely has a lot of history and is an old town. They also both have beaches if you are looking for that as well. Then on the way to Tennessee, you can swing by Ashville, NC, which is an awesome place. Lots of good food and breweries.