for the hot bit: rash vest and boardshorts for use whenever you are swimming/diving, bikini for on the beach (obviously stay in the shade). cover ups for evening against insects. One fleece for air con/the plane. Flip flops, gallons of sunscreen, insect repellent. Whatever you wear in the evening (it is NOT necessary to take a different outfit for each night!)
for sightseeing: comfortable trainers/walking shoes (not boots, too hot), big hat, cool cotton stuff such as t-shirts, long-ish shorts. The trainers/shoes will then work in New York.
for NY: layers of fleece, warm hat, gloves, scarf if you like, waterproof coat/jacket. Warm trousers (not jeans!) for the ice-skating, thermals underneath. Probably thermals at all times anyway!
Thank you! This may be a silly question, but I was thinking, is NY really fashionable and will I feel crap in tourist clothes? Obviously I want to be warm, but also don't want to feel scruffy if everyone else is dressed up!