Mr. Ruddy has hosted Mr. Carr and Laura Ingraham, another conservative radio host who supported Mr. Trump, at the club and has introduced Mr. Trump to a range of news media figures, politicians and donors. He described the president-elect as “seeking the pre-election Donald Trump: totally at ease, very positive, very gregarious.”

Mr. Trump appears to feed off contact with the people at the club.

Over the Thanksgiving holiday, he queried dinner guests about whether he should appoint Rudolph W. Giuliani or Mitt Romney as his secretary of state (he ended up picking neither).

During this trip, he has heaped praise on his ultimate choice for the job, Rex W. Tillerson, the head of Exxon Mobil. (Mr. Trump has called him “Mr. Exxon.”) He talks about the work he has done to find a solution for the problems at the Department of Veteran Affairs, which included a recent meeting with a number of executives at Mar-a-Lago. Mr. Trump told a New York Times reporter that he intended to make Brian Burns, the businessman son of a confidante of Joseph P. Kennedy, the ambassador to Ireland.

Isaac Perlmutter, the reclusive head of Marvel Entertainment, is a Mar-a-Lago member who helped Mr. Trump put that meeting together. Mr. Trump has also held sit-downs with Robert K. Kraft, the owner of the New England Patriots and a club member, and hosted prominent figures like Carlos Slim, the billionaire who is Mexico’s richest man.

Mr. Trump; his wife, Melania; and their 10-year-old son, Barron, inhabit a residential area of the club. His adult children and their families usually stay in nearby cabanas on the property. Mr. Trump frequently dines on the patio, a central point of action, where at night a singer plays with a small band, sometimes belting out requests from Mr. Trump and other guests. (“My Way,” a song popularized by Frank Sinatra, was one recent choice.) A violinist sometimes moves among tables, plucking tunes like the theme from “Fiddler on the Roof.”

Mr. Trump has given the cadre of White House reporters who now cover him some access to the club, but grudgingly so — he once again eluded the reporters covering him on Saturday, slipping away without any warning to play golf at another of his clubs nearby in Jupiter.