Best bet would be something like Liberty Landing, on the NJ side of the Hudson right across from Manhattan, so you can watch the parade from your berth. Easy PATH train trip into Manhattan also.
Staten Island will be way less convenient. IIRC the river and parts
of the bay are shut down entirely at times, so location counts.
The Jersey marinas
get a lot of wake action from the river traffic, so it isn't peaceful, but the open anchorages
are the same, and worse if the weather
is bad. And since it is NY harbor...if you anchor
, it may foul. Inconvenient if you're planning to set out on a passage