This was the first time the model was photographed since news broke about her split from Cook, the newspaper said.
She met with Cook and his parents, Jean and Harry, for about 15 minutes, according to the paper, and later appeared with Alexa, her 20-year-old daughter with Billy Joel.
Earlier this month, a publicist for the model confirmed that Brinkley and her fourth husband were separating. At the time, her publicist said in a statement to the AP, "her immediate concern is for her children, and she's hoping during this obviously difficult time that people will be kind enough to respect her privacy."
It later came to light that Cook, 47, an architect, had had an affair with 19-year-old ex-assistant Diana Bianchi. Then, singer Samantha Cole claimed she had an affair with him before he wed Brinkley in 1996.
Since then, Brinkley has been dodging the spotlight and the headlines with her children Jack, 11, and Sailor, 7. Her friend, entertainment reporter Jill Rappaport, told the "Today" show earlier this month that Brinkley fled somewhere with "no computers, no phones … she just wanted to put (the kids) where they could be shielded from all these horrible headlines."
Brinkley, 52, who was not wearing her wedding ring when she was spotted on Tuesday, would not comment to the newspaper.
"I'd rather not comment," a happy-looking Brinkley told the Daily News. "I just don't want to fuel this anymore."
Sources told the New York Daily News that Brinkley is finding it hard to forgive Cook for playing around and will likely divorce him.
Cook apologized to Brinkley in the July 25 edition of the New York Post. "I'm sorry. I'm contrite. I'm stupid. Foolish. No excuse," he told newspaper columnist Cindy Adams in a statement.
By Amy Bonawitz