Even on a slow day the Vince Lombardi doesn’t have enough parking (and that’s if you’re even near the NJ Turnpike).
Lombardi is entirely MYO spaces. I even found a spot when they shut down New England from that storm last winter.
When ever i had deliveries to do in the big smoke i'd always park up about 100 miles out of town then drive straight in to the receivers early in the morning never had an issue with parking or annoying the neighbours.
That might work if you only have one stop in NYC, but if you have multiple stops that will eat up your DOT clock fairly quickly just getting to NYC.