Don't do the GW bridge unless you want some real excitement. It will be a white knuckle high traffic experience with narrow lanes and lots of cars zipping in front of you.
I-684 to the Tappan Zee bridge works well.
From the Tappan Zee bridge, you could just stay on I-287 and do an easy bypass of the very busy Garden State parkway (depending on time of day). I-287 is essentially a beltway around the most congested traffic area in New Jersey. You can take it all the way to the NJ Turnpike. It will be the least stressful way. And possibly the fastest depending on time of week and day.
If you do take the Garden State Parkway, watch out for low bridges on the Garden State Parkway - some older bridges are made with stone arches and have low clearances in the lanes nearest the shoulders. They are marked in advance, but you will need to pay attention and avoid the right most lane to keep things from getting too exciting.
Have fun on your adventure.
Ed
