But for some visitors, the real draw was not transparency, or even the newly inaugurated Mr. Cuomo. It was his girlfriend, Sandra Lee, the Food Network star, who for a time greeted guests alongside him in the mansion’s cavernous receiving hall, in front of a fireplace festooned with oversize Christmas bulbs and pine cones.
“She introduced herself as Sandy,” Rochelle Filler, 45, of Glenmont, a suburb of Albany, said, beaming. “She was very down to earth.”
Another woman gushed that Ms. Lee told her she had already found three restaurants in Albany that she particularly enjoyed.
Which three? a reporter asked. The woman bashfully admitted she was so star-struck that she forgot to ask.
People leaving the mansion tended to mention Ms. Lee almost as much as Mr. Cuomo — either because they were disappointed they did not get to meet her, or because they were practically giddy about getting to shake her hand.
Carol Robbins, a teacher, and her husband, Richard, an information-technology specialist for the state’s corrections department, who live in Columbia County, most wanted to greet Ms. Lee, whose television program they watched together, or former Gov. Mario M. Cuomo, who, like Mr. Robbins, attended St. John’s University.
They did not meet either of them, but the younger Mr. Cuomo was an appealing consolation. “I’m hoping he’s going to do a good job, too,” Mr. Robbins said.
The open house drew hundreds of visitors, and for two hours, Mr. Cuomo and his lieutenant governor, Robert J. Duffy, enthusiastically greeted them.
Some people walked from a few blocks away; others shuffled into cars and drove hundreds of miles. Some had visited the governor’s residence as long ago as the Rockefeller administration, which ended in 1973; others had never set foot inside its rooms.
Jeanne Crane and Lorie Longhany drove four and a half hours from western New York for a minute or two of face time with Mr. Cuomo. Then they piled into the car and drove right back.
“When you’re from a small county, many times you don’t get recognized,” said Ms. Crane, the Democratic chairwoman of Orleans County. “A lot of times people say, oh, you didn’t get invited because they don’t care about the small counties. So I think it’s very important that we show up.”
In keeping with what seemed to be an unwritten bit of etiquette at the meet-and-greet, Ms. Crane and Ms. Longhany did not use their brief time with Mr. Cuomo to lobby about issues facing western New York. Instead, they did the only thing that felt right: they congratulated him.
The tradition of the open house goes back more than a century. Former Gov. Theodore Roosevelt was said to have shaken the hands of 6,000 people after his inauguration in 1899, with 2,000 others unable to get into the mansion. (The incoming Cuomo administration limited the number of guests to 300 and conducted a lottery to select them.)
Some who turned out on Saturday had made attending the events something of a tradition: they recalled meeting former Govs. Nelson A. Rockefeller and Hugh L. Carey there or offered opinions on which administration provided the best tour. (The verdict seemed to be that the tour on Saturday, which was constrained to a few rooms that were guarded by a maze of velvet rope, was less than ideal.)
Others arrived with the intention of thanking Mr. Cuomo for his positions. Claude Gruener, 69, and his partner, Doug Ponisi, 52, who live in Albany, a short walk from the mansion, wanted to thank Mr. Cuomo for his support of gay rights over the years. An economic development consultant came to give Mr. Cuomo a pep talk of sorts as he prepares to wrestle with the state’s huge budget deficit.
But politics was not the only thing on many people’s minds. Many parents brought along their young children to meet the governor, hoping that they could look back on it some day.
Reporter access to the open house was limited, leaving television crews at the foot of the driveway to chase visitors for quotes as they exited the mansion.
One child, who appeared to be about 3 years old, was already looking past the Cuomo era. She shared her own ambitions with a solicitous television reporter: “Someday,” she said, “I want to be governor.”