Petersburg and the Petersburg Battlefield just south of Richmond.
There's a great science museum in Richmond
Airborne and Special Operations Museum near Fayetteville, NC
(There are other sights there as well)
Santee, SC has a pretty good outlet mall if you're into shopping.
Mighty Eight Air Force Museum near Savannah, GA exit, I believe it's just north of it, but you can see it from the highway,
St. Augustine, Fl has a ton of sights and an easy trolley tour that you can jump on and off of to stop and see what interests you.
And you can get even more ideas here: