MLS Listings Rivertowne Mount Pleasant SC | Homes for sale on MLS in Rivertowne Subdivision. Homes For Sale in Rivertowne Neighborhood Mt Pleasant SC. Rivertowne golf community of Charleston SC is a country club development also in “north” Mount Pleasant and the homes for sale in Rivertowne will offer every buyer just about anything they could be looking for from varying price points. There are moderately priced homes, expensive waterfront, and riverfront homes in Rivertowne for sale, as well as homes on the golf course. View all homes for sale in Charleston SC golf course communities if you don’t find what you’re looking for here.