“Congrats on getting into the LLM at NYU! And getting the job in London! Those do sound like great offers. Would any of the other positions that you applied for in London come with funding?
As for the job market in New York, my impression is that it is very difficult for foreign students to get jobs after the LLM. This is largely because it is such a competitive market and you would have to work for a big firm most likely in order for them to be willing to sponsor a visa - but the firm jobs are pretty few and far between since there are so many American lawyers running around. That said, I'm not sure what the approach is in the public sector. What would be your goal in getting another LLM in the US? Do you want to live in London or New York in the long term?
In terms of waiting to hear from other universities for their international legal studies, I would wait on Harvard and Yale. Both of them are so well regarded and have exceptional international law. Furthermore, they have been big in the legal market for longer and I would imagine have better career services to help the LLMs get employment. Though neither is in New York, it would be cheaper and easier to be a student in New Haven or Cambridge.
I don't know if volunteering for a year first would make much of a difference in terms of jobs after, unless this is a position that you would consider taking fulltime. I'm not sure how helpful I'm being but I don't think you can go wrong."