Lake Titicaca near Puno

Yes, set in southern Peru, it's navigable and it has about 40 islands, two of them populated by welcoming Indians: Taquile and Amantani. The islands have no roads, so neither cars nor bicycles have ever passed by. Indians wear bright colored clothing and use the tortora reeds to built both their homes and boats. The legend says the founders of the Incan Empire themselves, Manco Capac and Mama Occlo, emerged from Lake Titicaca.