Gettysburg to Atlanta help

Trying to plan our route from Gettysburg to Atlanta in June. Since the National Parks don't have RV hookups (pet on board) we would like to find somewhere nice to stay a couple days in route to Atlanta. Looks like a lot of parks thru Virginia, along or close to I-81. We much prefer to stay off of the Interstates, so would appreciate route recommendations also. Would also like to hear about parts of the Blue Ridge Parkway.
Thanks,
Rod & Jane