You would have to prove that the hotel either created the dangerous condition or had actual or constructive notice of it. As for damages, I don't think a sprained ankle warrants the time and costs that goes into the lawsuit.
Consult with a personal injury attorney. There is a difference between getting no-fault coverage and being able to recover for pain and suffering. To get pain and suffering you need to show you suffered "serious injury" as defined in the Insurance Law.
A .20 is very high.
I would be careful about broadcasting that you called in a favor... someone can get in real trouble.
You should hire a criminal defense lawyer. I can't imagine a judge would let you plead guilty to a crime without a lawyer.
Under NY law, the car that stuck you in the rear is presumed negligent and will have to give a non-negligent explanation for why the accident took place. The most often given is the car in front made a short or sudden stop. Judges usually reject that defense. Another popular (and more successful) one is that the lead car suddenly changed lanes directly in front of the car causing it to rear-end the lead car.