Of course a city with a surface area of one square light year doesn't have to be one light year square. One light year square is 5,878,000,000,000 miles by 5,878,000,000,000 miles. Thus a square light day would be about 16,093,086,000 miles by 16,093,086,000 miles, a square light hour would be about 670,545,200 miles by 670,545,200 miles, a square light minute would be about 11,175,700 miles by 11,175,700 miles, and a square light second would be about 186,200 miles by 186,000 miles.
If the city was built in 365 layers each a mile apart, it would be 365 miles tall and 16,093,086,000 miles by 16,093,086,000 miles.
If the city was built in 8,766 layers each a mile apart, it would be 8,766 miles tall and 670,545,200 miles by 670,545,200 miles.
If the city was built in 525,960 layers each a mile apart, it would be 525,960 miles tall and 11,175,700 miles by 11,175,700 miles.
If the city was built in 31,557,600 layers each a mile apart, it would be 31,557,600 miles tall and 186,200 miles by 186,200 miles.
Suppose that all the buildings in the city are the same, relatively low, height, the better to somehow support the different layers.
If the layers are each 1,000 feet apart, the city could have 525,960 layers and be 99,613.615 miles tall and 11,175,700 miles by 11,175,700 miles.
If the layers are each 100 feet apart, the city could have 525,960 layers and be 9,961.3142 miles tall and 11,175,700 miles by 11,175,700 miles.
If the layers are each 100 feet apart, the city could have 31,557,600 layers and be 597,678.85 miles tall and 186,200 miles by 186,200 miles.
If the layers are each 10 feet apart - a single story - the city could have 525,960 layers and be 996.13636 miles tall and 11,175,700 miles by 11,175,700 miles.
If the layers are each 10 feet apart - a single story - the city could have 31,557,600 layers and be 59,798.863 miles tall and 186,200 miles by 186,200 miles.
Clearly the problem of communicating within such an impossible to construct city will be lessened by building it in many layers.
Note that the United States of America does not have three levels of government. It has four levels of government: Federal, State, County, and Municipal.
In the early Roman Empire there were four levels: the lowest levels were Pagi (plural of Pagus) country administrative districts within civitates or self governing city states, Governors supervised the city states in their provinces and the Emperor supervised everyone. In the later Roman empire there were six levels of government: Pagi, civitates, provinces, (secular) dioceses under Vicars, four prefectures under praetorian prefects, and the Empire under the emperor or emperors.
If a city has a surface are of one square light year or about 3.4550884 X 10 to the 25th power square miles it will need many layers of government. For example, if the smallest government units cover one square mile each, and each higher layer rules ten smaller areas, then there will be 25 levels of government. If each government unit rules one hundred units on the next level below it there will be about 12 levels of government, and so on.