NW side has improving outflow and definitely looks like a decent sized eye trying to pop on the vis: https://www.tropicaltidbits.com/sat/satlooper.php?region=08L&product=vis
https://www.tropicaltidbits.com/sat/satlooper.php?region=08L&product=vis
You can see a decent sized eye trying to clear just a bit on the vis. Outflow is improving on the NW side as well.
At this point northern NJ, NYC, western LI would see a rainy/breezy day. The real action would perhaps be along and east of the William Floyd Parkway in terms of wind.
If you are looking for wind you have to be along and right of the center of course. As the system becomes extratropical, the wind field will expand even as the max sustained winds decrease.
Got to love the warmer half of the year ;). Anyway it is snowing today in the NC mountains and 47F in Raleigh NC midday which is very cold here for May.