Get your Depends on. There pretty much are none.
You cannot get into the hotels without a key card specially printed for people staying over NYE. And yes, they check.
Stores close because the city requires everyone to be out before 3pm or you get locked in - and most of them close their bathrooms because people are drunk and disgusting (they're also mysteriously "closed for maintenance" on St. Patrick's Day, Puerto Rican Day Parade, and July 4th).
And I'm 99% sure that even if McDonald's and Hard Rock are open, they're going to require a purchase of more than a coffee to use them.
Even before all the recent events there have not been port-a-potties brought in, so they're sure as heck not bringing them in now.
AND once the holding pens are at capacity, that's it...no one else getting in that one. So you get in and stay in. (And the closest ones to the action are going to be full well before noon.)
Like I said... Get your Depends on.