Known to its founders as the Diminishing Republic, and to legend as Palm Tree Island, this sandbar has been a cultural hub for 20 years. (Port City Daily/Preston Lennon) WRIGHTSVILLE BEACH –– Nancy Faye Craig walks from her townhouse in Wrightsville Beach down to a small shore in her private neighborhood that faces the mouth of Lees Cut — Harbor Island’s northern saltwater border — through which small craft can cruise between the Intracoastal Waterway and Banks Channel. It’s a Saturday afternoon and the tide is dead low. Families who live in the townhomes that dot Wrightsville Beach’s edge — near the public boat ramp — read magazines and watch their children play in the water.