Well, Scott, have a great time and you'll have to give us
a report. The Myrtle Beach area is so developed that I have
stayed away from it for many years now, so I can't tell you
where to look or what you might find.
I doubt you will be finding any gemstones, or many rocks
for that matter, but shark teeth and fossils are always a
possibility down there. Just guessing but I would imagine you
would have to head south to the Pee Dee or north to the
Cape Fear to find areas remote enough for good hunting.
Shorelines around bridges are sometimes good places to check, otherwise you can just see what the tide has
washed in.
Watch out for gators!

Joe

If you can't find anything better maybe try the shoreline at Myrtle Beach State Park or Huntington Beach State Park. I have found teeth/fossils at both and they are less combed over that the shores right in Myrtle Beach.