The rumored couple visited the venue for Mellencamp's performance on with Willie Nelson.
Brinkley and her new beau stopped by Chalk Point Kitchen for some late-night eats after the appearance.
They have one child together, Sailor Lee Brinkley, born on June 2, 1998.
They divorced after revelations that Cook had slept with his 18-year-old office assistant.
Joel married his fourth wife, Alexis Roderick, in July, and the couple welcomed daughter Della the next month.