Yes, you can sue the city if you fall on the sidewalk.  The City must have "actual notice" of the defect in the sidewalk, and a claim must be filed with 90 days of the occurrence. It is only worthwhile to sue the City for a fall on the sidewalk is you have sustained a very serious injury.  This is because litigation against the City is expensive, and the investment is not merited unless there are enough "damages" to collect.