If you're in Hilton Head, I would definitely play Harbour Town as it is one of the most fun courses I've ever played. It isn't long, but it is very tight and it takes a while to get used to the course. You need to be on the correct side of the fairway or you might not even have a shot at the tiny greens. IMO every hole starting with 13 to the end could be a signature hole. It has beautiful par 3's and the 18th hole is very tough/fun.
I wasn't that impressed with Long Cove. It was a nice club and everyone treated us well, but if I had my choice I'd play Harbour Town, which I think is a much better course.
I haven't been able to get on at Colleton River, just off the island at Hilton Head, but it looks great. Haven't made it to May River either, but it is on my list to play sooner rather than later.
If you care to head South from Augusta, you could hit Jacksonville and try to play Sawgrass. I think Sea Island isn't too far either...maybe an hour south of Savannah.
Finally, even if you don't get a chance to play at Kiawah when you're near Charleston, go have lunch out there and check it out. Beautiful. The course will beat you up pretty good...it did to me anyway.
Have a great trip!