Ok. Sounds like an exciting tour. If you just do overnights at interstate 'in and out' places and avoid destination places, you will probably be fine Sunday thru Thursday. If you want scenic camping or destination camping for several days, you may have a problem. Summertime is busy in places with mountains, oceans, rivers and lakes while kids are out of school.
Your destination, Beaufort, is beautiful, historical and is likely to be crowded. There is a state park there on the ocean. Here you will need reservations, if you can get them. Not too far up I 95 is Charleston. Major history here, Fort Sumpter, plantations, the market, and Battery. If these things interest you, make reservations.
On up I95 is Savannah, GA, another historical stop and worth a tour.
Depending on your route, up i95, I would not miss Williamsburg, Jamestown, and Yorktown which have been reconstructed. More plantations. Early colony history and revolutionary war history here. Also Busch Gardens if you like that sort of thing in Williamsburg. If you are headed for the north western part of VA, there is the Shenandoah Valley national park. West VA has similar beauty.
in Tenneesse there is lots of mountain beauty (and whiskey making). A favorite place for many is the Smokey Mountains and Gatlinburg area. Mountains in the east are not as high or rocky as they are out west. Everything will be very green with vegetation. Creeks, rivers, and waterfalls in the Great Smokey mountains national park.
if you are going to drive this far, then there is much to experience. Bring mosquito repellent!
Pam