I actually did get to the NYC Atheists table on Saturday but I don't think I have enough material for a full report. Instead I will just write the little story I tell to define atheism. I'm often using it because I am arguing with these "militant" agnostics over semantics.
Everyone is born an atheist. How could we not be? We know nothing about any kind of gods or supernatural deities. These atheist babies grow up, learn to talk and start communicating with other people. At some point young people hear a story about a god. If these baby atheists believe the story, they are now theists. If they don't believe the story, they remain atheists. In other words, atheism is the default position.
So many people disagree with this definition. They think atheism is the "faith" that no gods exists. They claim I (and most other self described atheists) are changing the definition. I don't know if we are or not, but it doesn't matter. This basic definition of equating atheism to non-theism is more useful. Making atheism equal so called "strong atheism" makes the word useless.
Anyway, it all depends on the definition of "god" under discussion. First I'm an ignostic. For the purpose of argument over vague descriptions of gods I am an agnostic. For definite god models based on ancient myths I am an atheist.