Neyer won the United States Olympic trials in both springboard and platform diving in 1980, but did not participate in the 1980 Summer Olympics in Moscow because of the American-led boycott arising from the Soviet Union's 1979 invasion of Afghanistan. She was one of 461 athletes to receive a Congressional Gold Medal instead. Neyer accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, where she competed in National Collegiate Athletic Association (NCAA) competition as a member of coach Randy Reese's Florida Gators swimming and diving team in 1982, 1983, 1984 and 1986. As a freshman in 1982, she was a member of the Gator women's NCAA championship team that included swimmers Theresa Andrews, Amy Caulkins, Tracy Caulkins and Kathy Treible, and won her first two individual NCAA championships in the women's one-meter and three-meter springboard events. In August 1982, four months after her first NCAA championships, Neyer won the gold medal in the women's springboard competition at the World Aquatics Championships in Guayaquil, Ecuador.