As an All-Metro D.C. selection, Nance averaged 16.7 points and 12.4 points for Joe Den Davidson's Dunbar High School team. He guided Dunbar to a 19-5 record his senior year, a 29-0 mark, and the top prep team in the nation honor his junior season, followed by a 25-3 record as a sophomore. He was also an honor student with a 3.4 grade point average and graduated 14th in his class.

At WVU, Nance played 18 games in the 1977-1978 season, tallied six points and six rebounds against CCNY, and averaged one rebound per game in the 1977-1978 season. Nance worked his way into the starting lineup 11 games into the 1979 season. He concluded the game with a 7.4 scoring average and was also credited with 5.2 rebounds per contest. Nance scored in double figures on ten occasions in the 1979 season with his career high of 20 points coming against Duquesne. He also had 30 steals and 12 blocked shots. Greg Nance majored in economics.