I'm not sure I understand why anyone would want to hike to New York City. You might be able to catch some of the Northland trail, but most of the time you would be hiking along the side of highways. And then you'd be showing up in the largest metropolis in the US all smelly and dirty.

Twenty miles per day for thirty days is doable, but it's a bit ambitious for a group of novices with heavy gear. Even on relatively flat ground. Of course the flip side is that you could probably hitch a ride on the route you're planning.