Why did cities in the United States grow rapidly in the decades following the Civil War?
All cities of the Northeast and Midwest.
The Southeastern states post-civil war were still largely agrarian in nature and the large city was rare. Key to that area were Savannah and New Orleans, the key port cities of the south.
The industrial north and mid-west, not having endured the ravages of war, simply continued what they had started and grew far more rapidly because they could sell their wares upon the world market place. Conversely, the south did not have that advantage of large scale factory output and therefor did not grow nearly as rapidly.