I would recommend studying and learning as much as possible, and networking with people, both in and out of the university in one’s filed, as two most important aspects of an LL.M. program.
Both NYU and NYC have taught me numerous life and professional lessons.
NYU has the best arbitration courses (both commercial and investment treaty) which I was looking for.
One of the biggest plus points for me has been developing this network of friends all around the globe who are all doing extremely well. No doubt it is a great asset to have from a business perspective, but it holds far greater value to me personally.
I recommend gaining some experience before an LLM degree. It also gives you clarity about your interest areas which helps you to design your LLM program accordingly.