The 24-year-old Oscar-winning actress and the 38-year-old Coldplay frontman ate lunch at Tavern on the Green, People reports, before taking a stroll together at the park. The magazine also reports that the two visited Strawberry Fields -- a memorial to John Lennon -- at J. Law's request, then went to the Carlyle Hotel, where they spent the night.
"They talked quietly and seemed very happy," a source tells E! News about their demeanor.
Meanwhile, the 42-year-old Gwyneth stepped out with her man, 44-year-old television producer Brad Falchuk, at Robert Downey Jr.'s 50th birthday bash Saturday at the Barker Hangar in Santa Monica, Calif. After mingling with fellow A-listers such as Jennifer Aniston and her fiance, Justin Theroux, their date night continued on Sunday, when the two reportedly grabbed dinner at Chinois On Main in Santa Monica, Calif.