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Not to throw a wrench in your thoughts but in NY it is usually much less expensive to form and maintain an S Corp rather than an LLC. The publishing costs far exceed the filing fees for a corporation and the annual costs are also less costly with a corporation. You will also not need a registered agent. An S Corporation election using Federal form 2553 available at www.irs.gov and a CT-6 available at www.nystax.gov are easy to complete.
The publishing must be done in the county in which the LLC will operate and if you relocate it to NYC after setting it up in Albany you will need to republish.Also, you cannot start doing business until after the publishing is completed for the LLC whereas with a corporation you can begin doing business the day it is filed in Albany.