I have a business in NY State, as an LLC. My understanding is if I am taxed as Sub S, I could file for unemployment. Is this true? If so, which (additional) forms do I need to complete?

The first question is: did your LLC hire you as an employee and formally withhold federak and state income taxes and FICA taxes?

Second, while employing you, did your LLC pay state unemployment taxes?

If the answer to both is YES, then you probably can claim unemployment benefits.