I fell and broke my ankle at a city park. Is the city liable to pay? I don't have insurance

As I am licensed in Florida and Vermont, I cannot comment specifically on Iowa law. However, generally,you must show that a land owner breached a duty of care owed to you and caused your injuries. There may also be some specific Iowa statutes that restrict suits against cities and may provide them with immunity for a suit. Based on the content of your question, there does not appear to be any negligence on behalf of the city and therefore you would not likely recover. If there is more to the incident than what is described in your question, I would respectfully suggest that you contact an Iowa personal injury attorney as soon as possible and provide him or her with all the details.