Kirsten... go for it! NYC will be very hot, so to cool off, suggest lunch at the Boathouse in Central Park and an air conditioned visit to MOMA.
Even in the UK we have heard about the new High Line, which is said to be fantastic, although may be better to visit early morning, or late afternoon.
I did a round the island trip, but can't remember from which pier exactly (west side I think). The trip was about 3 hours, very interesting and saw a completely different side of NY. Thankfully, it was quite windy and cooling.
A tip... I found the air conditioning too cold, so consider taking a layer with you.
Apart from the excellent TA destination forum for New York, suggest you get hold of a Time Out guide. There really is so much to see and do, you won't be bored.
And.. Grand Central Station has fantastic restaurants, especially if you like fish/shellfood.
Once you have done New York, then London should be your next stop!