I am not licensed to practice in Florida, so I will answer based on general principles of law.
To fully analyze your claim a lot more facts are needed. Just because you fell it does not mean that someone has to pay. In order to recover you would have to show that the city was negligent and such negligence caused you fall. In fall cases, basically you would have to show tha the city knew a dangerous condition existed and failed to act reasonably in responding to it.
Plus, there may be immunity issues since it is a government entity.
A lawsuit based on someone else being responsible for negligence needs to be established by conduct that was unreasonable under the circumstances present. I would say yours is not a matter for the courts because the park may be immune from lawsuit liability for tort.
But....you should phone a lawyer in your locale to see if someone is willing to take you on as a plaintiff.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
Good luck to you.
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