Yes you can start your LLC in another state. You will need a registered agent in the other state. You will also need to register your LLC in NY to conduct business there. Since LLC's are not taxed as an entitiy it will not have that big of tax impact if you create the LLC in another state. I would suggest starting the LLC in your home state so you do not need to arrange to have a registered agent and you can work with your Secretary of State's office.
Thinking long term, you should consider a Delaware corp. Angel and VC investors prefer Delaware corps, because Delaware law would then apply to its governance, i.e., its internal affairs. More public corps are incorporated there than in any other state. It has the largest and best body of corporate law. Its law tends to favor management vis a vis its shareholders. The corp would then qualify to do business in NY. LLC’s are not favored by VC’s. They are not permitted to grant incentive stock options, which are tax favored under IRC Section 422 and commonly used for the rank and file. Nonqualified stock options, used for executives, are probably available.
If you are serious about seeking VC investors, do not try to economize. You need good corporate lawyers who are experienced in securities laws as well as Delaware law, and can handle a private placement of shares. Otherwise the VC’s will not take you seriously. An NYC law firm would be a good idea . You could start with a small firm, but eventually you will have to switch. The big firm will just insist on doing the corporate work over again to get it right.
If you are set on the LLC form, Delaware would be a good place to form it for some of the same reasons.
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(Bryant) Keith Martin