Yes you can walk across the George Washington bridge.however I really don't know where you can park on the New York side other than trying to find some place on the street or pay for a parking garage wherever you can find one. You have to know the parking regulations in NYC, like alternate side of the street parking. Read the signs carefully so you don't get tripped up. You don't want to get towed away or a ticket. You'll be sorry if you do.
Look where you can park off the bridge. It shouldn't be so far away.
On the NJ side there is plenty parking
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