I formed an LLC in NY in December 2020 which had no assets or activity in 2020. Do I need to file a 1065 or NY return?

You do not need to file a 1065, but you would need to file in New York if any member is a partner:

Federal:

Every domestic partnership must file Form 1065, unless it neither receives income nor incurs any expenditures treated as deductions or credits for federal income tax purposes.

Entities formed as LLCs that are classified as partnerships for federal income tax purposes have the same filing requirements as domestic partnerships.

New York:

Every partnership having either (1) at least one partner who is an individual, estate, or trust that is a resident of New York State, or (2) any income, gain, loss, or deduction from New York State sources, must file a return on Form IT-204, regardless of the amount of its income