I am a lawyer in CT.  In most states, you will be able to sue however, the issue is where you fell  - i.e. whose property.  If you fell on city property the burden you have to prove is that the uneven side walk was the sole reason for your fall.  If this is the case, then you may have a casue of action.  The lawyer is going to need to see the sidewalk to determine what if any risks it posed.  I suggest to take you medical bills and pictures of the sidewalk to a lawyer.