I'd check with a CPA. Often you have to register your out of state entity when doing business in your home state, thus in the end you end up paying the same. NY state has a req where you need to publish any new LLC in the papers, thus if you are in NYC this can become very costly.
Remmeber LLC is pass through , including ~13.6% self employment tax, which you will probably end up paying in taxes if you go for a s corp.
Anyways look into the different fees states charge yearly to maintain the LLC and how much profit you currently or projected make a year. This will determine which option is the best in the long run.
Edit, s/c corp and LLC both provide a shield from your private assets its mainly depending on different taxes etc. LLC has self employment tax(thats why they refer to double taxation) and corps have hgher fees usually for payrill, taxes etc.
This is no tax advice and just my opinion so go talk to a CPA for detailed info.