If you pay for a taxi or a uber they will cost a lot. I suggest taking the path train from 33rd st to Hoboken then the light rail to 34th st in Bayonne. Then you would have to get a quick lyft or uber.
It doesn't get very close but another way to see it from Manhattan is to take the Staten Island ferry. It's free, you get to see the Statue of Liberty and the Tear Drop Memorial. Not the same as walking the park though. You lose a sense of scale.
Uber, Lyft or Taxi.
PATH - Light rail - Taxi is a feasible option as suggested by Josh. There is a ferry service to Manhattan in progress with in 1 mile from the location, it may be ready this fall, proposed round trip fare is $25 .
There is no transportation service to this area. You have to drive in and drive out I might suggest a taxi that's the best
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