NYC is known for a couple really good jewish delis - Katz and 2nd Avenue deli are the most popular. I'm a fan of the lesser known Ben's too. I'm a fan of potato pancakes, hotdogs and motza ball soup.
The 2nd Avenue Deli got some press in 1996 when they were robbber (follow the link for more info on that)and is well known today. I've eaten at the old location on 10th Street and 2nd Ave as well as the new location at East 33rd Street. I'm a fan and a friend of mine swears they have the best Pastrami sandwhiches of the Jewish Deli's. It's a modern restaurant with good food.
I've been to Katz's a couple times and there can be quite a line there at times. When you enter you are given a ticket, DO NOT lose the ticket. When you go to the counters they will right your price on it, when you leave you pay at the register. If you don't have your ticket I think you pay $5o. Katz's is best know from When Harry Met Sally - the orgasm scene. The decor is vintage.
My favorite place for motza ball soup is Ben's Deli. It's a modern restaurant with good food.
Which is the best? Depends who you ask and what you're getting. You can't go wrong with any of the deli's. If you want a calmer dining type experience the Ben's or the 2nd Ave Deli are a better choice. They're all a bit pricey, but the food quality is good and you'll get a good meal.