Hiya - there wouldn't be anything for you at the airport but there would be "delis" all over NYC that will be open on the day.
Presumably you are going to Manhattan?
No worries.
The "deli" is what one might consider a newsagent or cornershop. Just pop out of your lodging and follow your nose or ask someone .
The only place they'd be scarce would be right in Times Square but you'd only need to go to another avenue over.
Have a good trip.
Milk, etc