Most people probably would take the train all the way to the northern section of the Bronx to explore on a Saturday afternoon, but they are missing a beautiful neighborhood in NYC. Little Italy is a tiny community near Fordham University centered around Arthur Ave. In my opinion, Tino's is probably the best of the best in Little Italy. They have lists of authentic Italian sandwiches, whatever you are in the mood for--from mild creamy mozzarella, basil, tomato to spicy combinations of sliced meats and roasted peppers. They also have a few dozen different daily salads that are wonderful.
Although an hour away from midtown, it is well worth the afternoon excursion.