You are brave mande, there's no way you'd get me up in a helicopter! I've never flown in to Newark, only JFK, but taxis were plentiful and I imagine it's the same wherever you fly into, just get in the taxi queue it moves quickly. I have been out on a train from Penn Station which stopped at Newark, I think it was half an hour away, so I guess the journey in by taxi would be something in the order of an hour, traffic can be pretty heavy as you can imagine.
I've been to New York twice, first time when the kids were young, we stayed in downtown Manhattan and did a lot on foot as well as a tour on one of those open top London buses. We got off at Greenwich Village and wandered around there, also their SoHo (stands for South of Houston Street) much nicer than ours, lovely shops. On other occasions we went up to Central Park, saw the John Lennon memorial and the Dakota Building. Took the lift up to the 84th floor, I think, in the Empire State and if I remember rightly there was some sort of virtual ride in the entrance of the building that we went on. Also went out to Ellis Island and up the Statue of Liberty. We all fell in love with NY, there's something about the city that resonates, possibly because it's in so many movies we've seen.
We went again about six year ago, just the two of us, stayed very near Ground Zero, which is in the midst of the Financial District, we were able to walk down to the Seaport area. The Staten Island Ferry is free so we did that got off at Staten Island, not much there, but it's a nice experience looking back at the iconic skyline. I remember hating Times Square that time, older and far more jaded, it's just so garish, like Piccadilly in London but times a 100. Not for me! Also thought on that second visit New York's parks paled into insignificance compared to London parks, Battery Park in particular it's nothing special. One place I did like was the Museum of Native American Culture, I think that's what it was called, could have stayed there all day, but alas time constraints. Grand Central Station is a must, it's a beautiful building with lots of cafes and restaurants in the forecourt. Also think the Chrysler Building as well as the Empire State is quite beautiful, wandered into the entrance, all lovely walnut wood and very art deco When we finished that stay we took a train from Penn Station down to Savannah, Georgia, left 3 pm arrived 6 am, that's why I remember Newark it stopped there. That was one great train ride.
I hope you have a great holiday, NY is undoubtedly a wonderful city.