Desoto State Park or Cheaha State Park are both beautiful also check out Nocalula Falls in Gadsden, AL, this city park is one of our favorites. Birmingham area I would vote for Oak Mountain.
Desoto has many beautiful waterfalls. Could be a challenge to get to if we have a freak winter snow. Nice big modern sites with 50amp and full hookups.
Cheaha is the highest point in Alabama with amazing views. The campground is on the old side with smaller sites and rough roads in the campground. Full hookups. Since it is the highest point to the roads can get iced over quickly and it's a long mountainous drive from I20.
Nocalula Falls has a 90 foot waterfalls, black squirrels and other fun things to do. Full hookups with 50 amps and large right friendly. Again. Watch the weather as it also elevated and could have ice road conditions.