The New York Family Clinic is the fictional fertility clinic where some important events in Will & Grace took place.
During the second season, Will went to a sperm bank at 33rd to deposit sperm for his friend Claire. The name of the clinic was not mentioned but it is assumed that it is the New York Family Clinic as this is Nurse Sheila's first appearance.
When Jack McFarland was 17, he donated sperm at the clinic to buy a leather jacket. This eventually resulted in his son Elliot being conceived via in vitro fertilization after one of the nurses Bonnie "picked it up before they threw it away."
Later in the series, Nurse Sheila appears pregnant and states that she used one of the sperm donations to the clinic.