I can help with some of that.
I'm out in Berkeley County - pretty close to Charleston.
For regular old shooting, I'm not sure. There's a local gun club (
http://www.palmettogunclub.org/) that does various matches, but I'm not a competitive shooter so I haven't investigated it too heavily. I personally shoot at a range on Highway 41 (41 comes out of Mt Pleasant) - the Boggy Head Rifle Range. You can plink and shoot there for free as it's DNR provided. No sporting clays though.
As far as hunting - you looking to do public land or clubs exclusively? I mostly hunt public in the the Francis Marion hunt unit, so what I know is out there.
If you're looking for pigs, head on out to the Wambaw hunt unit. If you take Hwy 17 out of Mt Pleasant, then take of left onto Steed Creek Road, then a right onto Halfway Creek Road, you'll have the Wambaw Hunt unit on your right (Northhampton Hunt Unit on the left). Wambaw is crawling with hogs. If you want to shoot with your pistol you're fine during deer season. Hogs are considered a nuisance animal, so you can hunt them year round with whatever you want, so long as something else is in season, and whatever weapon you have with you is legal for the other animal in that area. So, since deer can be hunted with handguns, you can hunt hogs at that time with handguns. If it's turkey season (spring), you can hunt hogs with turkey loads, etc, etc. Same rules apply to coyotes (legal to hunt and shoot whenever something else is legal). In particular if you want to hunt coyotes a .22 Magnum comes in handy here, since as a rimfire it stays legal for use throughout small game season. Note that all this applies to public lands only. On private lands, you can hunt hogs and coyote year round with whatever you want.
For deer, Hell Hole WMA is pretty good. It's down Highway 41 in the same area as the range that I mentioned earlier. Except for one day per year, they keep the dog hunters out of Hell Hole which keeps the area calmer than most other areas. Waterhorn also has no dog hunting all year, but I've just never hunted much over there.
For ducks - there's two choices: woodducks in the swamps, or river hunting. Throw on your waders and head into any of the swamps and you can kill your limit in woodducks just about every time. They're good eating ducks, but if you get tired of that head out onto some of the marshes on the Cooper River. Putting in at Cypress Gardens will get you about where you want to be. Get out into the marshy fields and you'll see a lot of action.
Can't help you on doves or turkey. I don't hunt either that much. My father is REALLY into turkey hunting, but he tends to be pretty tight lipped about where the birds are
.
PS Attached is a pic of a fairly large hog that my brother got behind his house about 4 weeks ago. It's on private land, but it's embedded right inbetween a lot of the areas mentioned above. There's some really good hog hunting around here if you're into it.
