Question for changing address

I live in New York City Now. Which I know that I’ll pay Federal, New York State (State) & New York City Tax (City/Local). Which I’m Pending to Move To The Nassau County which don’t have local tax. But If I Move To Nassau County But My Job Is In Flushing, New York City. Which is a drive of 20-30minutes. How would I pay my taxes? Do I still need to pay local taxes?