Hilton Head Island has several excellent public golf courses. Some of the best ones include:

1. Harbour Town Golf Links: Known for hosting the PGA Tour's RBC Heritage, this course is a must-play with its scenic beauty and challenging layout.

2. Heron Point by Pete Dye: Designed by legendary architect Pete Dye, this course features strategic bunkering and beautiful Lowcountry views.

3. Palmetto Dunes Oceanfront Resort: This resort offers three fantastic courses - Robert Trent Jones Oceanfront Course, George Fazio Course, and Arthur Hills Course, all with their unique challenges.

4. Oyster Reef Golf Club: Renowned for its stunning water views and a memorable par-3 6th hole, Oyster Reef is a favorite among golfers.

5. Hilton Head National Golf Club: Known for its excellent value and diverse layout, this course provides a great golfing experience.

6. Shipyard Golf Club: With 27 holes and beautiful landscaping, Shipyard offers variety and challenge for golfers of all levels.

7. Palmetto Hall Plantation Club: Featuring two 18-hole courses designed by Arthur Hills and Robert Cupp, Palmetto Hall offers a diverse golf experience.

Remember to book tee times in advance, as these courses can be quite popular, especially during the golf season on Hilton Head Island.