Best resources for finding an apartment in Tribeca, New York City?

Craigslist is a good start. Try the "no fee" and "by owner" listings first to try to avoid the broker fee. In all honesty, you probably be able to avoid a broker because the vacancy percentage is so low right now, but it's worth a shot. If that doesn't work, go to "all apartments". You can find Tribeca, specifically, by clicking on Manhattan and filtering the neighborhood. Or, you can also go directly to a brokerage website. Citihabitats and Bond are two of the biggest.