Like
@Judique said, Folly Field is further out and will have less restaurants. Folly Field and Coligny Beach Park are both public beaches. Coligny Beach will be pretty crowded since there are lots of shops and restaurants right there. Palmetto Dunes is a restricted access beach, so you have to have a pass to get into the area.
We really like Palmetto Dunes and just rented a place there a few weeks ago since the Disney resort was closed. It seems like many of the condos were built in the 80s and some have been updated, but others haven't. There are a few restaurants in Palmetto Dunes, but we usually venture outside the resort area to eat.
Hilton Head is a great family beach area with lots of wonderful restaurants and biking trails. I hope you enjoy your trip!