Arlen, who is the 25-year-old son of McCartney's wife, Nancy Shevell, was all smiles during the outing, sporting a red-and-white Metallica hoodie with brown shorts and white sneakers.
McCartney also opted for a casual ensemble, donning a white jacket over a bright orange T-shirt, which he paired with black slacks, olive green shoes and a blue baseball cap.
McCartney, 75, and Shevell, 57, started dating in November 2007 and said "I do" in 2011. The lovebirds will be celebrating their sixth wedding anniversary in October. McCartney has five kids of his own -- Heather, 54, Mary, 47, Stella, 45, James, 39, and Beatrice, 13, from his previous marriages.