The Contest of Mayors has certain tasks that consist of improving buildings from Paris, London or Tokyo.
If you are using the trick of not creating buildings from these cities (Paris, London and Tokyo buildings may NOT be interesting), what you must do is to have a slot of 2x2 (or more) in your city to perform the tasks you get in the Contest of Mayors.
Once the task is done, you just need to destroy the building to have the space available again.