There's tons of minature golf courses, which is always fun for all ages.
If your kids like animals, there's also the Waccatee Zoo near Socastee and Alligator Adventure near Barefoot Landing. Links below:
Waccatee Zoological Farm - The 'Beast' Kept Secret In Myrtle Beach
Welcome To Alligator Adventure || Reptile Capital of the World!
There's a riverboat that leaves from a landing near the Waccatee Zoo. It goes down the Intracoastal Waterway and is a nice relaxing ride. Dick's Marina in Murrells Inlet has an excellent trip with lots of hands-on stuff for kids.
There's Brookgreen Gardens, with lovely flowers, sculpture, a riverboat and a small zoo. Tickets to here are good for seven consecutive days. Across the highway is the Huntington Beach State Park with a castle to explore (doesn't look like a European castle, though, and it's just empty). There's also Myrtle Beach State Park with a great fishing pier.
Carolina Jeep Safari Tours provides a nice trip with interesting narration, including some ghost stores, and some stops at places including Atalaya (the castle I mentioned above). You may even seen some alligators!
Be sure to check out the boardwalk area and there's even an amusement park, Family Kingdom, in the middle of town.
I could go on and on, but with the links by CT Yankee and some more research I'm sure you'll find more than enough to do.