I go from SYR to Jfk using 81/380/80 when I hit Jersey I start trying to get 1010 wins on the A.M. radio. I then decide which way is best based on their traffic reports very 10 minutes.
alternates are;

GWB to the cross bronx to 678 and over the whitestone bridge but the cross bronx can be backed up for a long way. It is also confusing and rough.

NEW JERSEY TURNPIKE TO Holland tunnel to either brooklyn, manhattan or williamsburg bridge and then278 to airport

or your verrazano alternate.l
Personaly I have the best uck with the Holland tunnel route but I know the turns to take now. also I can fill up on that cheap Jersey gas just before the tunnel.

STAY OFF 17 (piece of sh_t road) yuck!!!

By the way my gPS always routes me through the lincoln tunnel then through the queens midtown tunnel to 495 to 678 but I do not like that route.

I make my decision based on what the radio tells me is happening on the bridges and tunnels. Sometimes one is backed up and another is wide open.

I do the trip 5-6 times a year.
Good luck

By he way there is a WAFFLE HOUSE in Clarks Summit now