Legal Question in Business Law in New York

File only where you are doing business.

As you have property in NY you must file. You also cannot pursue any NY based claims unless your LLC is registered in NY.

As to NH, is any business actually done there? Speak to a NH lawyer to get the correct answer as there are many possibilities.

Re: Foreign LLC Application

In most instances, to "conduct business" in any state (other than the state of incorporation or formation), a foreign entity must register with the foreign state.

Owning and managing real property is likely to be considered conducting business.

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Re: Foreign LLC Application

NY will probably consider your llc doing business in NY so do register as a foreign entity in NY; the cost is minimal. But you remain a domestic company in NH.