Like the guy above me said, check out the Alligator farm. That place it awesome. There are these two huge gators or crocs that are ginormous and they have tigers and other animals there too.
Murrell's Inlet is a nice area to visit with stores and a pier and restaurants. Not sure if I spelled Mural's Inlet right though. Here is a link. They have a gift shop store across from the road from the water and there is actually a live alligator that somehow got into this little water area where some people are likely to roam, so watch out for that. lol.
http://www.murrellsinletsc.com/
Then there's dinner shows like Dixie Stampede and shows like Legends. They also opened a theme park last year as a Hard Rock Cafe theme park but it since changed names and is under new ownership. I think it's off George Bishop Highway in South Myrtle Beach.
Dino's House of Pancakes on Highway 17 in North Myrtle Beach is a great place for breakfast.
Tons of mini-golf and go cart places. Barefoot landing and the board walk are popular places at night with shopping, and restaurants and live entertainment. I think the boardwalk does a fireworks show every night.
You could also go into NC being it's only like 15 mins outside of N Myrtle Beach to get fresh seafood when the shrimp boats come in.
I know these things cause I just came home from there like 4 weeks ago. A week flies by even faster when you are down there compared to home.