Fratellis. A lot of places claim to serve NY pizza. This is the only place that smells correct the second you walk in. It's the no-question #1. If you are a NY transplant, it's the closest you'll get.
St. Francis Apizza. New Haven style is not quite NY style, but it's also not so different. This place has the freshest ingredients in the city and you can taste it right away. Tons of flavor in the sauce, crust, and cheese. Its a cliche, but you can just taste the quality and care put into every pie.
Brooklyn. This one may be controversial, but when I want something great but don't want to head up to West chester or down to HP, this hits the spot. Authenticity 7/10. Very good.
Not mentioned (but not bc I haven't tried them): Trophy, Two Cities, il Gusto, Goodfellas, Adriaticos.
Of all of these other, Goodfellas is my fave ,but more like what a Midwesterner thinks NY pizza should be like than authentic tasting. I'd eat the crap out of it still!
Edit: adding guardia and Mad Anthony's on my list to try.