Conkey, the eldest of five siblings, graduated from Mount Holyoke College in 1965 with an ancient history and art history double major, and shortly got the chance to go to Jordan - in what is now the West Bank - to work in biblical archaeology. When she then submitted graduate applications to the anthropology departments at the University of Chicago and the University of Pennsylvania, she was told she needed to take a year of undergraduate anthropology (which was not available at Mount Holyoke College) before they could grant her a final admission. She and a friend then spent a summer in New York, where she obtained a job with the Wenner-Gren Foundation for Anthropological Research as a librarian and eventually became a grant analyst. When accepted at the Oriental Institute, she went back to Chicago to attend and work a part-time job as an editorial assistant at Current Anthropology.