mr. mike,
I've done it a couple of different ways. 1st question are you driving straight thru? if yes then you want to go with option 1...if not option 2.
Option 1) Leave NY at 9:30PM (yes PM)...you'll need to sleep all day and get up at about 7-7:30 PM and have breakfast (NOT DINNER, it'll throw off your body into realizing it is actually night time. This should get you to WDW just in time for Check-in at 4PM (18 1/2 hours no rain and occasional traffic for construction etc. - no "legal-counseling sessions" either)
Why leave at night you ask. Mainly because after 18+ hours of driving the last thing you are going to want to do is hit the parks, and with "official" check-in time at 4:00 PM, you don't want to risk getting there too early, not getting a room and not being "physically too tired" to go to the parks to kill some time. For me it worked perfectly, got our room, checked-in, unpacked, had an early dinner and then a good night's sleep... giddyup you are ready to go in the morning.
Option 2) Leave NY at 4:30 AM, and stop over in Hilton Head (WDW Resort there) Arrive at HHI, approx 12-13 hours later, again just in time for check-in, unpack, dinner...sleep up early the next day for the relatively short 5-6 hour drive to WDW, and you are not wo wiped out that you don't mind killing the afternoon in one of the parks until your room is ready, come back and check-in later.
It really all depends on what your goals and your limits are for the long drive...for Option 1 it is CRITICAL, that you are well rested, and your co-pilot/co-driver can sleep during the night, so that at 6AM or so after the breakfast stop you can switch and then you can sleep/nap. The thing for me was that you get rid of the night part of the trip while you are fresh. The fact that you are tired during the day gets a little bit washed out with the adrenaline of being closer to WDW, at nighttime you get more psyched out due to the darkness.
Hope that helps, good luck and drive safe!