BLUE RIDGE, Ga.—When former New Yorker Marty Stefanelli and his wife contemplated retirement, they didn’t know where to look until a visit to this Appalachian mountain town last year.

“We bought a house that week,” Mr. Stefanelli said. “I need to find time to wind down, and Blue Ridge forces you to wind down.”

For the 57-year-old Mr. Stefanelli,...