Thom has a good route. From Montgomery, AL we have gone that route, but prefer: Birmingham, Nashville, TN., Paducah, KY., St. Louis, MO.. Kansas City, Sioux City, IA., Sioux Falls, SD., then straight across the state going by Wall, The Bad Lands, Rapid City, SD.
Have made this trip several times and really enjoy the area. Have fun and may God keep you safe.