No. As far is as known from records on both sides, no German U-boat crews ever went ashore in the U.S. At one point they did drop off saboteurs (in New Jersey and Florida I believe) who were quickly captured, and I think I remember reading somewhere that they might have landed in Canada at some point.
There are rumors that a bread wrapper from a U.S. bakery was found on a captured U-boat, but since U-boats used to scavenge supplies from boats they boarded and sunk, this is the most likely explanation if the story is indeed true.
The closest thing that I know of to this story was during Operation Drumbeat. According to Gannon's book on Drumbeat, Reinhard Hardegen of
U-123 was so close to New York city that he could see the buildings, lit up bright as day. Made sinking ships easier since they were silhouetted against the bright lights!
As for docking in NYC, go ahead and try it. I guarantee you won't get a warm welcome to the Big Apple.