Try the Congaree National Park.
It's the largest intact expanse of old growth, bottomland hardwood forest remaining in the southeastern United States - and it's about a 25 minute drive from downtown Columbia.
First, it's totally free. No fees for anything. The park is open 24/7, every day of the year, but Saturday is the best day to go. Pretty much every Saturday there's a guided tour of some sort. And yeah, the tours are free, too. Some require reservations, others don't.
If you're not into planning or reservations, you can just show up and walk the boardwalk loop, which is a (roughly) two-mile loop comprised of a raised boardwalk through the swamp that starts and ends at the Visitor's Center. It's great for families, as the boardwalk keeps the children focused on going one direction, rather than wandering off.
During famously hot days in Columbia, you can go on a paddling trip from one part of the Congaree river to another through the National Park. Toss a cooler in the canoe and you've got yourself a whole day on the river. If you're in a Boy Scout troop in Columbia, this is a must do.
If you want to see what South Carolina looked like a couple hundred years ago, go check it out. It's like stepping into a time machine. It's free and it's closer than you think.
