Magic circle
As someone with limited experience at Magic Circle, (I have been there once) I would not imagine it to be a hard thing to find a place to camp on New Years Eave. It is a very large place, there are not dedicated pre determined camp spots, Just a lot of land that you pull up to an open spot and set up. You will need to pay the BLM fee for daily use at the entrance of the Long Term Visitor Area, I don't recall what it is off hand.
Thanks for the info. I have been there during the off season and my original question was to determine if there might be an empty square of BLM dirt that would be large enough for me to park or would it be really packed do to the holiday, and it sounds like the answer would be yes. Unfortunately due to the gov shutdown I was not able to go for New Years, maybe next year. Again thnx for the great feed back. No threads rules!