The meat packing District is above Greenich Village and is the home of the Chelsea Market (9th ave & west 15th street) as well as high-end celbrity chef restaurants like Del Posto & Morimoto. If you're more the biker bar type there's Hog & Heifers on Washington.
I took the Chelsea Market food tour a couple of years ago...here's the link to that post. It's a historical commercial area that is being cleaned up with the intention of keeping some of the architectual flavorings of the past. (or so they said on the tour)
Chelsea Market tour post