Look at these flights. The prices rely on a 30-day advance purchase.
I didn't take the 6:00AM flight since the connection is too close. Flights to Newark cost slightly less, but the cab ride more than makes up for it.
When you leave the plane, follow the signs to baggage claim/ground transportation. There you will see signs for the taxi stands. You have to wait in line at the taxi stand - it is not allowed to just flag one down. Tell the driver to take you to 75th St. between Columbus and Amsterdam in Manhattan. The building is much closer to Amsterdam. Look for #160 on the left-hand side (gray on the bottom, brick on the top, not very wide, the door is below street level.) Have around $25. in cash ready for the cab. The cost includes around $19. for the trip, $3.00 - 3.50 for the bridge toll, and a 15% - 20% tip.