The premier walking and biking site in Columbia [1] is the excellent Three Rivers Greenway (803/765-2200, www.riveralliance.org [2], daily dawn–dusk, free), actually an umbrella project comprising three separate riverwalks on the banks of the Congaree and Broad Rivers, most directly connected. There are lighted and paved trails, boardwalks, and overlooks all along the nearly nine-mile collective Greenway, and future extensions are underway.
All paths are ADA-friendly; you can even take baby strollers along with no problem. Designated public parking is available at all entrances to the Three Rivers Greenway.
The key segments on the east side of the rivers, closest to downtown, are Granby Park (accessible via Huger St. past Blossom St. and onto Catawba St.) and Riverfront Park (accessible via Huger St. to Laurel St.). While at Riverfront Park, you can see the remains of the city’s 1906 waterworks.
On the other side of the rivers in West Columbia and the suburb of Cayce are the West Columbia Riverwalk (from town, cross over the Gervais Street Bridge, take a left on Alexander Rd., and you’ll see the Amphitheater and parking lot on the left) and the Cayce Riverwalk (take Blossom St. over the river, a left onto Axtell Dr./Jessamine St., and the entrance is on the left).
Harbison State Forest (5500 Broad River Rd., 803/896-8890, www.state.sc.us/forest/refharb.htm [3], free) features over 12 miles of trails through the hardwood forest down to the Broad River.
A 14-mile segment of the ambitious, state-wide Palmetto Trail (www.palmettoconservation.org [4]) cuts through Fort Jackson on the east side of town. Access it through Gate 1, where you can park your car at the trailhead.
Links:
[1] http://www.moon.com/destinations/south-carolina/columbia-and-the-midlands/columbia
[2] http://www.riveralliance.org
[3] http://www.state.sc.us/forest/refharb.htm
[4] http://www.palmettoconservation.org