If you're looking for one of, if not, THE best Italian deli, you can't go past Raineri's. The business is now run by Joseph Raineri, 3rd generation of this family business, but inside this store time seems to have stopped. Here I can find products that I remember from my childhood in Italy, when I used to visit my grandparents are their little grocery store.
Raineri's offers a wide range of products: oils, pasta (both well known brands and the past they make), cheese, canned goods, cold meats, sweets, dried fruit, coffee, you name it, they have it! And it will taste nothing like in the supermarket.
While you wait in line to be served, you can enjoy a tasting of various cheeses, cold meats and oils. Among the cheeses, it's a must to try (and buy) some pecorino, both spicy and normal. Also, ask the friendly staff for some grated parmesan: they will grate it on the spot for you and it's so cheap! You'll never buy parmesan at the supermarket again!
Honestly, why would you go shopping anywhere else when you have a bit of Italy right here?