Veterans Pier, beside Captain Dick's in Murrells Inlet is free and has become a pretty popular spot for both fishing and crabbing. Not sure what the "catching" is like.

About 1/4 mile north of the entrance to Huntington Beach State Park, there's a little dirt road with an "oyster recycling" sign. There's a small beach at the end of the dirt road that's a popular fishing spot. If you drive a little further South to Pawleys Island, there are two causeways that go to the island from Hwy 17. The bridges over the creek are also popular spots. You'll need a saltwater fishing license to fish from any of these spots. As long as the kids are under 16, they don't need one. Good luck!