Well, you probably won't have much luck with good courses near Myrtle Beach.
Socastee Rec. Park is the best one I've played while on vacation there, and it's not even finished yet. It looks very promising so far, but teepads haven't been installed
and the entire course is covered in spider webs.
East Bay Park is also fairly close (at least, it's close to where I always stay, if you're staying on the Grand Strand then I'm not sure). This one is pretty much only useful if you just need to get out and throw a disc, the layout isn't very impressive and the mosquitoes are vicious.
Also, if you don't mind paying to play, and you want to play when it's a bit cooler out, then you might try
Tupelo Bay. I haven't played this one, but it seems to be a decent place to get a round in, if you don't get golfers yelling at you for playing frisbee on the course.
Myrtle Beach really doesn't have much to offer for disc golf, but at least it's not totally devoid of courses. Also, I've read about leagues going on at Loris Nature Park, which is about 30-40 minutes away, so if you don't mind driving that's still an option. Last but not least, check out the
Myrtle Beach Disc Golf facebook page.