2 days to Austin TX on the trailer. You can visit the grassy knoll along the way. Get on the bike, head to President Johnson's ranch then hit the Three Sisters and circle back to the trailer.
Oh, and see the bats at dusk in Austin.
Wing it, no pun intended. Watch the weather forecast and drive to the weather. You may get a shot at the Ozarks that time of year. Otherwise you are looking at having to be south of Atlanta. No roads there.
How much time do you have?