I looked up the writers and directors of the two episodes where Harry's South Carolina birthplace was mentioned (
VOY: Eye of the Needle and
One) and none of them that had birthplaces listed mentioned being from South Carolina, though it's possible that they moved there later in life.
Jeri Taylor wrote the teleplay for both
Eye of the Needle and
One, and wrote the novel
Pathways where Harry was further clarified to be from Monterey, South Carolina ("Monterey" is probably why so many people were confused and thought he was from California, because of the famous Monterey Bay and aquarium there), so it's safe to assume it was her idea. Taylor was from Bloomington, Indiana (Captain Janeway's birthplace) and went to school at Cal State Northridge in California, but perhaps she moved to South Carolina later in life or had pleasant vacation experiences there or just threw a dart at a map to choose Harry's birthplace.
There's no actual town of Monterey in South Carolina, but there is a Monterey Bay Suites resort in Myrtle Beach, so I suspect someone had a nice vacation there and wanted to give them a shout out in pre-Yelp days.