Good recs above. I'll add:
Sara J's (Garden City)--very popular, so get there early to avoid the wait.
Russell's (Murrell's Inlet)--no pretense, just the freshest local seafood expertly prepared. Atmosphere is like sitting in the comfy den of an old fishing lodge.
Bubba's Fish Shack (Surfside)--Great "beachy" atmosphere, fun for the kids.
And of course, Calabash is always worth the drive--Seafood Hut, Ella's, Dockside, and Beck's are highly recommended.
Bubba's Fish Shack
16 S Ocean Blvd, Surfside Beach, SC 29575
Are you serious? I live on the Grand Strand and I very rarely eat at any chains. With over 1500 choices of places to eat it is easy avoid them.
A few of my favorites are:
Salt Water Creek Cafe, Dockside,Bliss,Prossers and Lee's Inlet Kitchen in Murrells Inlet, Chive Blosson in Pawley's Island, Sea Captian's House, the dining room at Island Vista, The Library in Myrtle Beach.
Lee's Inlet Kitchen
Highway 17 Bus, Murrells Inlet, SC 29576