I'm a little more cautious/skeptical than the other people in this thread. Let me start off with my background. I graduated from Wesleyan University for undergrad, worked for a couple years, then got my master's in IR from the LSE this past year.
I am a bit confused by your concerns, thebrittzditz. Are you saying you are going to Stern as an undergrad? What impact does this have on your major and non-major requirements? Could you double major or take a minor? What about opportunities to take classes in other NYC schools?
My thought is that you might be getting a little too wrapped up in the specialization aspect of Stern v. LSE. Would an NYU undergraduate program really require to forego the "pick and choose" feel of most other liberal arts colleges? A couple friends of mine did Wharton undergrad but didn't really have to deal with this issue too much. I would really go over the requirements carefully. I think the hallmark of US programs is that they don't ask you to specialize, very much unlike UK programs, which gives you a lot more freedom to tackel your interest in IR.
Also, it seems like your main concern, as Hughski remarks, is job prospects after graduation. I work in IR, and believe me, Masters, internships, or no, it's a difficult market, at least in DC. You'll be getting out in a minimum of three years, so the economy could change drastically, but just keep in mind that 1. IR jobs don't pay that well, 2. IR jobs don't necessarily require a Master's, and 3. This probably shouldn't be a significant criteria in deciding what school to go to. I agree with Hughski: go with what you think would be more fun. You sound like you really don't want to be at Stern studying business, but the scholarship is attractive, as well as the fact that Stern is well regarded. So, go over the requirements with a fine-toothed comb. Are the course requirements flexible enough that you can adjust things to how you like it? If not, why don't you go to LSE to pursue something you apparently really love? Just know that, at least in this economy, you might be putting yourself at some disadvantage if you decide to return to the US. But, that all depends on what you do with your time in school, and it's by no means insurmountable. It could very well be a solid springboard instead.