Bankhead National Forest would be a better destination.
I've spent a little time in the Bankhead NF and so here's a little background on it. It's the best chunk of forested land in NW AL and kinda unique that hemlock reaches it's southern range here. Forests look much like the southern Appalachians. Topographically it's not hilly but not quite mountainous. No really steep grades on the roads. Most of the roads are maintained dirt and gravel forest service roads. You could drive your grandma's Camry if you wanted, or yours if she wants to keep hers clean

. Even you guys without a real Land Cruiser (100 and 200 series


) can negotiate the roads

. There are a few old logging roads scattered about that would require 4WD and present the potential for some pin-striping but these tend to be tucked away and usually end in a dead end.
I'm only familiar with the Brushy Lake campground. It's not large, camping fee is $5, restroom, water, picnic table are available. It'll shut down in about a month but will still be open. All this means is that the FS locks the bathroom and turns off the water but the campground will remain available. There are other campgrounds in the forest but I have no experience with those. Since this is a national forest camping does not have to be confined to a FS campground.
Plenty of places for hiking. The Sipsey Wilderness is a popular destination. Trails run along Sipsey Fork and Brushy Creek, the two major streams in the forest. The geology is caprock of sandstone over limestone providing great conditions for the creation of small waterfalls.
Canoe floats can be done on both Sipsey Fork and Brushy Creek but only when water levels are up some. Both floats are ca. 10 miles total.
US Forest Service headquarters is in Double Springs, AL and that's the place to get a map. AL hwy 33 runs north from Double Springs to Moulton. Dropping off the plateau when nearing Moulton someone along the east side of the highway has an old FJ40.
An old cemetery tuck away in the forest.