Hello Hannah, and welcome to SMNetwork.
First of all, it is not easy to get started in NYC, especially as a new stage manager. Also, we do things a little differently here in the States so you will need a minute of transition to learn the difference before taking work here. There are things we do that you don't and vice versa, and aspects of stage management that are handled by different levels than in the UK.
I suggest you look around this site a bit and, among other things, check out some of the previous conversations on this topic - I have listed 4 of, well, many - and you can type either New York or Broadway into the search engine to see even more discussions, B'way being the mecca for so many of us.
http://smnetwork.org/forum/index.php/topic,5555.msg33853.html#msg33853http://smnetwork.org/forum/index.php/topic,5390.msg32776.html#msg32776http://smnetwork.org/forum/index.php/topic,4064.msg24701.html#msg24701http://smnetwork.org/forum/index.php/topic,4291.msg33336.html#msg33336And keep in mind, there are many, many SMs of varying experience all vying for work in NYC. You will want to start as a PA if you can get that work (your accent will take you far, as Americans are suckers for that lilting British dialect) although that, too, is precious in NY.
Good luck and let us know how it goes (and if you land in the catbird seat, there will be mass envy by those who have struggled to be noticed for too many years!)