The Newark Air Tran is a free monorail that will take you to Newark Penn Station.
From there, you can change to NJ transit into New York Penn Station
I also think that you can change to the PATH trains and get to downtown NYC. I know the PATH also goes midtown, but you might need to transfer. Haven't ridden that in years.
If you want to take a cab from Newark, I would book something with a fixed rate. Even though it might be "close" miles wise, there could be a ton of traffic and it could cost a lot of money.
From there, you can change to NJ transit into New York Penn Station
I also think that you can change to the PATH trains and get to downtown NYC. I know the PATH also goes midtown, but you might need to transfer. Haven't ridden that in years.
If you want to take a cab from Newark, I would book something with a fixed rate. Even though it might be "close" miles wise, there could be a ton of traffic and it could cost a lot of money.