New York State requires that you publish a notice of formation of the LLC. That'll cost at least around $700. One good service that I'd recommend, if you do, is interstatefilings.com; it can handle filing the formation certificate and publication of the LLC.
New York State is very anti-business. Unless you're "doing business in New York", you don't have to set up or register your LLC in NY, and you can pick a friendlier state, such as Delaware, which is very easy to deal with.
If you have specific questions about what constitutes "doing business in New York", which will trigger a requirement that you "qualify your LLC to do business" in New York (and thus pay for the publication), please ask.