An interesting way of visualizing the changing fortunes of American cities is at this graph of metropolitan population ranks over time, compiled by Greg Slayden. Some notable trends:
– The most “turbulent” periods appear to be the western settlement in 1820-1860 and the rise of the Sunbelt in 1970-1990
– Dramatic movements appear just as often as stable oscillations, particularly when cities appear or disappear from the list
– The only city that appears on the Top 20 list, disappears, then makes a comeback appears to be Seattle

Might be interesting to group the cities — say, regionally, to see the rise of different parts of the country.