The answer to this question really depends on what caused the broken piece of sidewalk. For example, if a truck was rolling by and the sidewalk was in reasonably good condition, but the pressure from this truck driving on the sidewalk caused it to break, then the claim is perhaps better brought against that truck owner for causing the broken sidewalk. However, if the broken sidewalk was due to negligent maintenance or construction by the city, then you may have a claim against the city for that type of negligence.
One other thing I’d like you to keep in mind is that you only have a limited time to give notice to a city entity. In the state of Florida, you have four years to bring most accident claims. However, if your claim is against the city, you have to give them notice of an intent to sue within three years. Because these notice requirements can be complex, we really do recommend that you contact an attorney to discuss your legal rights