The house has served as the official residence of the city’s mayor for 75 years. Every mayor but one (Michael R. Bloomberg) has lived in the house since Mayor Fiorello H. La Guardia moved there in 1942. While Mr. de Blasio and his wife, Chirlane McCray, live in a private residence on the second floor, they also use the mansion for business, which means the house is a beehive of activity.

As we wandered past wreaths and strings of Christmas lights, aides shuffled through stately rooms. The kitchen staff sent out ginger tea and prosciutto-wrapped melon for a meeting between the first ladies of New York and Anchorage, Alaska. And Paul Gunther, the executive director of the Gracie Mansion Conservancy, which maintains the house, stopped by to welcome us.

In years past, Mr. Gunther told us, the first lady has traditionally acted as a hostess and greeter and concerned herself with the comfort of the first family, the running of the house, and its décor — including the holiday decorations.

“I certainly have not confined what I do to those tasks,” Ms. McCray said in an interview. Her $850 million mental health initiative, her independent nonprofit group and other work have made her arguably the most influential first lady in our city’s history. “I would say the role that I play at Gracie Mansion reflects the person that I am,” she said.