Actually, NYC's Greenmarkets have done a really good job of addressing the issues of food access. They're one of the organizations working the hardest in this country at the moment to get at the heart of the access problem. They have 51 greenmarket locations.
Greenmarket Farmers Markets | GrowNYC
Here's a list of locations that take EBT cards to get tokens (how SNAP benefits are administered at farmer's markets):
EBT/Food Stamps and Food Access in Greenmarkets | GrowNYC
And here's an article from the AP that covers the farmer's market/SNAP benefits issue:
The Associated Press: Farmers' markets draw few food stamp users