18Z Euro (2nd image only through 7 AM Tuesday) shifts northwest with the snow:
The 1st image shows the projected snowfall through 7 AM Thursday from the National Weather Service model blend. It gives a good general idea of where the axis of heaviest snow should be, although max amounts will likely be higher.
My general thinking for Long Island is 6 to 12 inches with low to moderate bust potential for now.
The 18Z Euro run only goes until 7 AM Tuesday, but it has trended northwest with the snow. Keep in mind that the 2nd image ends at 7 AM Tuesday.