Looking to volunteer or donate to a food bank? Need their services? Below are some great organizations. Also consider one of the options on the city's map: 
Food Bank For New York City has a bunch of spots to donate/receive food. Find the closest one here:
Here's their volunteer opportunity calendar: 
The Bowery Mission (227 Bowery) is another great food dispersing organization. Here's their volunteer page: 
Camba (21 Snyder Ave in Flatbush) does great work. Volunteer info here:
Hour Children (36-11 12th Street in Dutch Kills) accepts/disperses food from 9 to 5 M-F.
Here's their volunteer info page:
Part of the Solution (2755 Webster Ave in the Bronx) accepts/disperses fresh, frozen or canned food, prepared food, toiletries, diapers, baby formula & wipes & cleaning products.
Here's their volunteer application:
Project Hospitality (514 Bay Street in Staten Island) accepts/disperses food from 9 to 5 M-F.
Here's their volunteer application:
West Side Campaign Against Hunger (263 W. 86th) is a great option for those on the Upper West Side.
Here's their volunteer info page:
New York Common Pantry has locations at 8 East 109th and 1290 Hoe Avenue in the Bronx.
Here's their volunteer calendar:
City Harvest (6 East 32nd) does great work rescuing food that would otherwise be thrown away. Learn more about helping them out here: