I have always taught that you may not carry a concealed weapon in a publicly owned place - period. I have recently found that this may be in error. Conversations with SLED agents indicate that the most conservative interpretation of State law is to not carry a firearm in any publicly owned place.

The Statute controlling this now reads;
SECTION 16 23 420. Possession of firearm on school property; concealed weapons.
(A) It is unlawful for a person to possess a firearm of any kind on any premises or property owned, operated, or controlled by a private or public school, college, university, technical college, other post secondary institution, *or in any publicly owned building, without the express permission of the authorities in charge of the premises or property. The provisions of this subsection related to any premises or property owned, operated, or controlled by a private or public school, college, university, technical college, or other post secondary institution, do not apply to a person who is authorized to carry a concealed weapon pursuant to Article 4, Chapter 31, Title 23 when the weapon remains inside an attended or locked motor vehicle and is secured in a closed glove compartment, closed console, closed trunk, or in a closed container secured by an integral fastener and transported in the luggage compartment of the vehicle. * emphasis added.
As this has been explained to me, if you have CWP you may carry a weapon in a publicly owned place (city or county park, sports area, landfill etc), as long as the weapon is not carried INTO a publicly owned building. For instance - you may carry at Boyd Pond Park, ODell Weeks Park or the North Augusta Recreation Center/ Greenway as long as the firearm is not taken INTO a building on the premises.

Despite this, there are many publicly owned, political subdivisions of the State (county and local municipalities) owned locations that post with some type sign stating that the possession of firearms is not allowed on the premises at all. This appears to be in direct conflict with S.C. state law
South Carolina is a preemption state, basically meaning that the State law supersedes any local ordinance.
Chapter 31 Article 7 section 510 of the SC Code states in full;