I was just in NY for the first time a couple of weeks ago and I ate at Carnegie Deli (7th ave near 55th street and Broadway), John's Pizzeria (44th between 7th and 8th ave) and Dos Camino's (Houston and West Broadway). I enjoyed all of them.
on the corner of Lex and 43rd (might be 44th) right across from Grand Central, there is a street vendor that makes the best chicken and rice you will ever eat. Ask for both the red and white sauce. I'm not kidding, this stuff should be illegal it's so good.
We enjoyed Foley's Fish House, which looks down on Times Square. Reserve early, get a table in the front window for best viewing. Food and service were exellent.
Also enjoyed a pre-theater dinner at The District on 46th, right off Times Square.