Incorporating in another state: home office tax deduction?
By registering your LLC in Wyoming, technically you would be able to operate your business from home in New York. However, by making such deductions as home office you would create a nexus of your business in New York, which would eventually require you to register it there as a foreign entity. That would bring you back to the problem of publication costs.
It would likely make the most sense to register your business in New York to begin with. The publication requirement can be expensive, especially in the 5 boroughs of NYC, typically between $1,500-$2,000. We developed a legal method of getting the publications done for $499, which saves our clients a ton of money.
You do have another option: You could consider registering your business as an S-Corp. This would have your company formed as a corporation, but elected to be taxed as an S-Corp, which is similar to an LLC as a pass-through tax structure, with certain self-employment tax advantages. In NY corporations are not required to do newspaper publications.
Keep in mind, an S-Corp will require more maintenance, such as drafting company by-laws, mandatory meetings and recording meeting minutes. Aslo, it's always a good idea to discuss the tax differences between an LLC and an S-Corp with a licensed accountant.