Oak Mountain, just south of Birmingham, is a delightful state park. It's convenient to the interstate, has full hook-ups, is beautiful, and has many hiking trails and other attractions. We've stayed there twice and enjoyed it both times. One family we know here in Pensacola goes to Oak Mountain as a destination, they spend a week there and thoroughly enjoyed it.
BTW, during the trip from British Columbia, (where we bought our new Escape), back here to Pensacola, the interstate leaving Birmingham to the south was the worst stretch of road we ran into for towing our new Escape
. The old concrete road was so bumpy that I swore I would never go that way again.