First trip to Myrtle Beach from LI thought I could do it in one haul. What an almost tragic mistake. The light on 501 was quick, my senses dull from 14 hours of towing. Both feet on the brakes and the TV stopped clean in the lane of traffic. After that it was never again. I95 southbound is Fredericksburg KOA. Its 8 hours from LI maybe a little more for you. Its a couple miles off the I95, quiet and peaceful.
Alternatively take 13 down through the DelMarva, cross the Chesapeake bay Bridge and grab 17 to OBX. Toms Cove CG in Chincateague is 8 hrs from LI.
Do yourself and all your going with a HUGE and SAFE favor by laying over someplace, before something really bad happens.
The KOA looked nice but Camp Hatterus CG got the best reviews. We stayed in the oceanfront portion one rig from the entrance to the beach. Would definitely go back.
Since that one big wakeup call, I never did that again and always make a reservation 8-10 hours at the max out and do the same on the return.Hopefully you will seriously consider it and we wont read about you in the news.
Happy Trails