I've always said that, for me, the thing that truly distinguishes New York City as a restaurant city from other cities around the country (or world for that matter) is the breadth of small, outstanding neighborhood restaurants there. This was especially true when I was in NYC recently and had an opportunity to dine at Frankies Spuntino at 17 Clinton Street on the lower East side. A satellite of another popular restaurant in Brooklyn (Frankies 457), this tiny spot, with probably no more than 20 seats, just happened to have some availability on a Sunday afternoon when the other restaurant we'd been planning to visit was unexpectedly closed. With its succinct Italian influenced menu, rustic decor and the cutest, closet-esque kitchen this chef has ever seen, Frankies was the perfect spot for some Sunday afternoon antipasti, Vino Bianco and pasta. Check out their website for more details and be sure to pick up a can of their fragrant house olive oil (also available at many NYC markets).
Frankies Spuntino: http://www.frankiesspuntino.com
(You must also visit the just opened Highline Park on the Lower West Side, pictured above: http://www.thehighline.org )