I just tried a route similar to Dr. Gridlock's (Washington Post) suggestion. I-95 to I-695 west around Baltimore. Take I-83 north to Harrisburg, Pa.. Take I-81 to I-78 and head into NYC that way. It's longer, but less stressful, and no tolls until you reach NYC bridge. It also takes about the same amount of time as I-95 and NJ turnpike.
Of course you'll need to find the way from 78 to NYC since I don't know the best way from there.