I'll be the third to recommend Ippudo, but add that in addition to being the best ramen place in NYC they also have the best steamed pork buns and some of the best wings in the city. I wouldn't leave without ordering all three.
The steamed pork bun at Ippudo are pretty good, but I have to admit that Momofuku has them beat on that point. The ramen at Ippudo is hands down the champion in NYC though. The ramen they serve at Momofuku doesn't come close; I almost prefer the packaged stuff.
Downtown I am not as experienced but I favor Jay's on 16th and 7th avenue as well as one on chambers and church who's name I can't remember for the life of me. It's on the corner right above the ACE so you can't miss it.
Dona Bella pizza?