Even if you incorporate in say Delaware, if you are physically present running your business in New York you must register your LLC there (Authority to Transact Business) which comes with the same requirements.
i honestly dont know about operating a us company from a foreign country but if you have two owners in two states you would have a primary state where you incorporate and the other state you would set up a foreign corp (basically says one company is working in a new state) additionally you could choose a third state like delaware then have a foreign corp in each of the other states