Charles Towne Landing is kind of one of those things that really only locals go to, which is nice because it cuts down on the crowding.
This is the site of the first settlement in Charles Towne back in the 1600's. There is a replica ship and town there, and if you go during the summertime, they'll have 'real life' reinactment people making soap and candles and stuff.
This is a huge park and has a zoo, too, with bears and aligators and raccoons. It's very nice.
Lots of picnic grounds as well.
Take a day and spend the time at CharlesTowne landing. Beware--this is a popular place for field-trips and daycares, so you may have to battle large groups of children to get to see anything, but it's really spacious so it shouldn't be too bad.