You could do the GWB, or NJ transit.
I actually commuted from Brooklyn to Rahway, NJ on ye olde Nj transit for a while.
I would ride over the Billy B into Manhattan and then meander over to Penn Station.
You do have to watch out for jerky porters.
If I had a nickel for every porter who told me, "Just wait until the people laod on".
And then they ignore you.
"My car is full", even worse.
They try to have 1 bike per car.
Some porters are cool.
And others . . .
I actually had a porter tell me "I don't let you bikers on my train."