Interestingly enough, the mean center of population for NY State is only about 9 miles from the NJ border. Given NYC's location, not suprising. I wonder if there are any states with centers of population closer to the border than that. Given NY's geometry, if NYC continues to grow relative to upstate, I could imagine the center of population of the state actually being outside of NY State boundaries.
It's also possible in the past the NJ's state center of population might have been in NY - if Newark and Northern NJ were more relatively populous, I think that the mean center of population might be in Staten Island or the NY-NJ harbor.