Chewacla State Park is a beautiful 700-acre state park near Auburn, Alabama about an hour east of Montgomery. The best park about the park is Chewacla Lake, a great spot to go canoeing, kayaking, or just take a dip in summertime. As it's a protected state park, they don't let you use a gasoline-powered boat in the lake. There are also a couple of streams in the lake for trout fishing.
If you're a hiker, Chewacla State park has you covered. There are eight or so trails for all abilities, my favorite of which was the Deer Rub Trail. It's a bit longer than some of the other trails like Sweet Shrub or Eagle Scout, but it takes you around the entire park and passes by the streams and waterfalls.
Admission, I believe, is only $3 for adults so it's a nice way to spend a family day without breaking the bank. If you've got a large family or group of friends, they also have really nice, quiet picnic pavilions which you can rent for around $50 and spend the entire day eating, drinking, and hanging out in the great outdoors.