If others in this thread are talking about the same thing I've been experiencing for months, I found an explanation:
http://www.nycwireless.net/2009/07/psa-free-public-wi-fi-is-not-a-free-wireless- internet-hotspot/
I selected "Forget this Network" for the "Free Public WiFi" option in the provider list on my iPhone and iPad and the option doesn't automatically come up. If you're a Windows XP user you definitely should read the article.
There is actually free wi-fi at many of the public parks in Manhattan. In lower Manhattan I often use several Downtown Manhattan Alliance hotspots at the Vietnam Veterans Memorial on Water Street and the English garden at Pearl and Hanover. The signal may load a little slowly, but those spots do work. I also use the one in Madison Square Park that appears as nyc.wireless.net in the provider list. You need to register for a free account, and the signal works best near the router, which is atop Shake Shack.
As another poster mentioned, Starbucks now offers free unlimited wifi with any purchase, and at public libraries and at all Apple stores in NYC wi-fi is always free.