Downtown Charleston is considered a very safe area. Historic District (from Broad Street, to Upper King Street, Mary Street, and slightly beyond) is bustling until midnight during the week and later on weekends. A lot of late-night crime is directed at those who drink too much, so if you'd had a few you might consider taking a taxi to your hotel. Lock your car doors, and don't leave valuables in sight.
Distribute your cash, credit cards, IDs, and other valuables between a deep front pocket, an inside jacket or vest pocket, and a hidden money pouch. Don't reach for the money pouch once you're in public.