We strongly prefer North Myrtle Beach over MB - wider and nicer beach, more family-oriented, less traffic and newer resorts. Still a short drive to all the MB entertainment and shopping but a much better beachfront resort area. It's easy to avoid all the hubbub of MB when staying in NMB so it works well for us. So much variety of things to do nearby.
Hilton Head SC is lovely, completely different, more green and it has wide, flat, packed-sand beaches. If your kids like the beach, pools, bicycling, sea kayaking, dolphin watch boat rides, horseback riding and nature walks, they'll enjoy HHI. There's plenty of golf, tennis, shopping and restauarants for the adults too, of course.
Edisto Island SC is supposedly quieter with pebbly beaches, good for quiet walks, boating and golf.
Isle of Palms SC is just minutes from Charleston - a golf community near nice beaches and perfect for daytrips into wonderful Charleston and surrounding plantations.
Virginia Beach has a long and bustling beachfront tourist district. We've visited several times from Williamsburg, an hour away. But the kids liked the whole t-shirt and shell shops kitsch of the area, along with the very wide beach. It's not my thing as I like quieter beaches.
Outer Banks NC has rougher beaches, steeper with a serious undertow at times. Not really a kid-friendly beach area, IMO, but terrific for sightseeing, walking, and teens/adults who like the beach. Gorgeous national seashore.
Haven't been to Jekyll's Island in GA since I was a little kid. Some people love it there though skeeters can be powerful in the height of summer.
And then there's Florida...