No fear of bears or lions unless you decide to hike through their enclosures at the zoo.
Riverbanks Zoo and Botanical Gardens are very nice and you should go. It is on the banks of the SAluda River and the convergence of the Saluda and Broad rivers into the Congaree. There are two walking parks also on the banks of these rivers. Riverfront on the Columbia side follws the canal, and the other is much newer and is on the West Columbia side of the rivers with an entrance at the West Columbia side of the Gervais St bridge. There is also the State Museum also on Gervais St at the river. The University of South Carolina is based here, and campus is spread all over the city. There is Harbison State park about 10 minutes up I-26 from Columbia that has mountain biking and hiking trails. It also has a canoe lauch as it is located along the Broad River. There are several companies like River Runner Outdoor Center that offer canoing trips. There is the Congaree Swamp National Park. There is Lake Murray with fishing, boating, etc. You can rent boats/waverunners from several places. There is Stripper and Trout fishing on the Saluda from Congaree all the way up the the base of the Lake Murray Dam on the Saluda, if the Strippers are running by then. You can walk around the Vista and Five Points, some of the local college hangouts. There is also alot of shopping in Haribison and at the Villages of Sandhills. You could take a day trip to Charleston (the Holy City) only about a 1 1/2 hour drive away. In Charleston there are Aquariums, Fort Sumter, The Yorktown and Patriots Point, Folley Beach, Isle Of Palms beaches, shopping, deep-sea fihing, etc. You could day trip above the Greenville/Spartanburg area to the mountians and Caesars Head, Jones Gap, Raven Cliff Falls, etc for trout fishing, hiking, 4x4, etc.
You are only here for 3 days so thats prob enough, if you want more though just shout! Give me an idea of what you want to see and I can help better. Places to shoot, history, etc. This is my 'hood.
-Hershey
Oh yeah, and I work in Foodservice so I can reccomend some restaurants too.