People have misconceptions that the weather on transatlantics will be rough as they go across the sea, but everyone I have spoken to says that it is really nice and calm and the sun out so you can get a suntan and it feels warm - and hopefully the weather will be nice in Southampton too..
August Weather in NY:
Average High: 83°F (28°C)
Average Low: 69°F (21°C)
August can be quite hot and humid, though it's a bit cooler and drier than July, especially later in the month.
What to Wear:
pack an umbrella
a light sweater or waterproof jacket (for keeping warm in the air conditioned museums and stores)
closed toe shoes, comfortable for walking and water-resistant, if possible
a picnic blanket is great if you want to check out some of the free concerts and movie.