Many believe that your new business is better served by forming the LLC in Delaware or Nevada to reduce costs and to avoid New York's publication requirement. If you intend to do business in New York using a LLC that was formed in another state, you must comply with the foreign LLC requirements under New York law. (Please see this article for a discussion about when an out-of-state entity is "doing business" in New York, or contact The Stowe Law Firm, LLC)
Among other things, your LLC will have to file an Application for Authority, pursuant to Section 802 of New York's Limited Liability Company Law (Section 1306 for a Professional Limited Liability Company). New York also requires that all foreign LLCs publish, just as a domestic LLC must do.