From Austin if you are heading for Little Rock you will go through the Dallas area and I'll skip talking too much about that although you might think about stopping off at Beiharz and Wilson Blocks in Dallas - 2 blocks on the National Register of Historic places. And also you might visit Old City Park On the way from Dallas why not deviate to Hot Springs which has the restored Fordyce Bathhouse (free). There is also a tower (for which there is a fee) Nearby is Garvan Woodland Gardens
In Little Rock itself I would visit Little Rock Central High School National Historic Site, and of course the Capitol, the Old Statehouse Museum, and the Clinton Library. The Governor's Mansion can be toured (with advance notice). There is also a Historic District downtown and several other museums.
From there you would go to Memphis and there is so much to do there that I will just mention that you can ride the old trolleycars. From there you might go up to Cape Girardeau and then go up the Mississippi to Sainte Genevieve which is one of the first towns settled in the area. The settlers were French. There is a Visitor's Center and some old houses that can be toured.