Palmetto State Shooting Center
Riverwalk Business Park, Okatie - about 20-30 minutes from anywhere on Hilton Head
Take 278W to 170E, follow about 3 miles. Riverwalk Business Park is on the left. Drive all the way to the back of the Business Park and you'll see it.
They're open 10AM to 6PM Monday through Saturday, except for Thursday (9PM), and Sunday 11AM to 3PM. Great indoor range, but handguns only.
There a DNR range in Richmond Hill, GA, that is free and open to the public from sunrise to sunset. It's a bit of a hike to get there, but it's an outdoor range. Depending on the day, you can have a nice, safe, well-run range full of military guys, or a downright scary range full of muzzlesweeping morons in overalls. BE CAUTIOUS.