Where'd you end up going to grab a bite? NYC can be a very friendly place if you plan it well in advance.
Well both of us being students and on on a tight budget we mostly went with the cheaper options such as sandwiches from subway and the likes. For breakfast we mostly ate the egg + bacon + cheese bagels that deli shops offered. At the hotel there was even a refrigerator in our room so we were able to have to milk stored there as well and drink that in the morning before we went out. It would have been nice to eat out at fancier places but the food bill adds up quickly when you are constantly buying food from shops for 8 days straight.