Greenbrier Island Campground, Great Smoky Mountains, Tennessee Pictures Greenbrier Island Campround is secluded and nestled in a peaceful valley bordering the Great Smoky Mountains National Park, surrounded by the crystal clear waters of the Little Pigeon River. They offer a camping experience from the most primitive Tent camping to the more advanced RV campsites.Greenbrier Island's swimming and water sport facilities for their guests is a swimming hole with a 'natural diving board' and fishing for all you Trout Lovers. - says: Sallie