What was a popular vending machine system for food in New York City?

The popular vending machine system for food in New York City is automats. Automats were dining establishments where patrons could choose their meals from a variety of pre-prepared dishes displayed in glass-fronted compartments. The concept became especially popular in the early to mid-20th century, offering a unique and convenient dining experience that combined elements of self-service with affordable pricing.

At automats, customers would insert coins into the machines to unlock doors and retrieve their chosen items, such as sandwiches, salads, and desserts. This innovative approach allowed for quick and easy access to meals without the need for a traditional wait staff, catering to the fast-paced lifestyle of New Yorkers.

While food trucks, street vendors, and delis all contribute to the city's vibrant food culture, they do not specifically represent the vending machine system that defined the automat experience. Automats unique characteristics of combining machine-based selection with a varied menu make them stand out as the correct answer in this context.