This is Princess Grace of Monaco, leaving New York on the SS Constitution to travel to Monaco for her wedding to Prince Rainier.
The SS Constitution was built in 1951 and sailed to Europe until the late 1960's when she started sailing to Hawaii. She retired in 1995 and was sunk in 1997.
Grace Kelly wears a beige suit by Ben Zuckerman, and she is seen carrying the Hermes bag named after her, the Kelly Bag.