1: Machu Picchu, Peru Few places capture the imagination like this archaeological site, a citadel built by the ancient Incas in the 15th century and mysteriously abandoned. Machu Picchu's network of dry-stone walls and agricultural terraces etch the mountaintop site, surrounded by Andean peaks. Throw in llamas and alpacas, who graze on grassy slopes nearby, and you have a winner.