Gotham City Hall is a town hall located in Gotham City. It is where elected officials and authorities make decisions based on events in Gotham. City Hall has been rebuilt several times due to destruction from criminals. It is usually located near the Wayne Enterprises building.
The previous Hall was destroyed by the Joker in an attempt to kill the Mayor. It seemed like an intentional attack on the Mayor's Office, but it was all just a plan for his breakout. After the destruction of the building, The Joker took over Arkham Island and was eventually stopped by Batman.
The new Gotham City Hall was being constructed while Hugo Strange was forming his master plan for the upcoming Arkham City. Meanwhile, Strange was developing T&T, which was formed from two members of Two-Face's gang. T&T made many crimes and raids on Gotham City. During the opening ceremony for the new Hall, Quincy Sharp, Gotham's new mayor (who was being mind controlled by Strange), was announcing the opening when T&T attacked the ceremony, killing many people and it destroyed the building. Another building was constructed and it is unknown when it was constructed due to the fact that it was completed by the time Arkham City was open. The council voted to approve Protocol 10 (by the manipulation of Strange). However, they expressed their anger at Strange for letting Arkham's inmates roam wild. Batman eventually stopped Protocol 10 soon after. It is unknown what happened to the Hall after the events of Arkham City.