Town Hall: Town Hall refers to the 23rd Police District.
Public Violence Mission: From what I gather, it sounds like the officers assigned to this mission look for gang bangers and stop them question them to find out who they are. They then turn in the info at the conclusion of the mission to their supervisor.
Top Ten Target Mission: Units assigned to this mission usually concentrate on the Sunnyside Mall and the Broncho Billy Playlot looking for known troublemakers and see what they are up to, looking for reasons to make arrests.