Aye Carumba!!! - New York will consider you re doing business in NY. Therefore, you will need to register your LLC in NY as well (and pay whatever taxes and fees are required).
You will need a sales tax permit in the states you do business in, not the one where the company is formed (incorporated) in. Business permits may or may not be required by NY law, but if you are doing business there you will need one if required.
I know you need it in California. :-)
