The golf course list goes on and on. If you want to stay close to the HHI resort, the Palmeto Dunes Plantation is right across the highway from the Resort. They have 3 courses, a Robert Trent Jones, an Arthur Hills and I think the third is a Pete Dye. I have played the RTJa nd AH courses. I didn't have my A game the day we played the AH course and it was brutal. Actually that day I had my "how many golf balls can you drown in 18 holes game". Tough course but very beautiful. We played the RTJ course the last day on the Island and again a very nice course. they had just finished a complete refurb of the course and it was super! We also played a couple of rounds at Palmeto Hall Plantation and a couple on the mainland. We didn't even scratch the surface. Sea Pines with Harbor Town is about 15 or 20 minutes down the road, but we decided not to play it because the greens fees were more than double the rest of the courses and one of my brothers was on a tight budget.
The folks at the resort can e-mail or fax you a list of courses and they usually have special rates available. They will also make tee times for you as well. At least that was the situation a couple of years ago when my brothers and I went