Kiawah Resort offers five fantastic golf courses that are open to all Kiawah guests. Tee time reservations are required, and the courses book quickly. The ocean course is touted as the longest and most difficult course in South Carolina. We personally think it is one of the most beautiful courses as well
Website: Kiawah Resort Golf

There are many public and semi-private golf courses in reasonable proximity to Kiawah. Below are some suggestions for off-island golf.
Website: Golf Pass - Golf Courses near Kiawah
Website: Charleston Golf Guide

Guest and family favorites:

The Links at Stono Ferry: Semi-private, fairly close to Kiawah, and the "home" course for the College of Charleston golf team. It earns a 4-star rating from Golf Digest but very reasonably priced and is usually in great condition.
Website: Stono Ferry Golf

Patriot’s Point: Located just over the Cooper River Bridge in Charleston, a few of its holes are along Charleston Harbor and are therefore quite memorable. The course gets a lot of play, so advance reservations are definitely recommended and due to the course traffic, course conditions are usually not as nice as Links at Stono Ferry.
Website: Patriots Point Links

Wild Dunes: Offers several public golf courses on Isle of Palm. A little further from Kiawah (about an hour to hour and a half drive, depending on traffic), but offers courses with beautiful views of the area.
Website: Wild Dunes Golf Links Course
Website: Wild Dunes Harbor Course