If you want a classic sit down NY coal style pizza like johns, Grimaldi's, Totonnos, Lombardi's or Patsy's a wood burning oven can get you there. If you want the classic slice style pizza such as Joes', John's Ben's, Rays, your best bet is actually a home oven turned all the way up either with a stone or maybe even better, with a pizza steel.
Most wood burning ovens tend to want to run hot and bake fast. That can be too much for the slice style NY pizza, but it can be done. These ovens are better suited to other styles baked in 4 minutes or less such as Neapolitan.