We went to Tybee Island last year...outside of Savannah, GA and we loved it!
It was less crowded than nearby Hilton Head...nice and clean. It had that "small-town" feel, but was still close to activities. We were amazed at how far we could go out and still be only to our waist. Also, there is a tide pool that runs along the beach that little ones were playing in. It was great!
Jekyl Island, GA was another nice beach, but we haven't been there in years, so I don't know how it is now...
Hope this helps...