I upgraded my PC to a Pentium 4 2.8 Ghz system, 512 Mb DDR Ram, with an ATI Radeon 9200 graphics board. Before that, playing larger maps with lots of cities made each turn take extremely long, and sometimes my entire screen went black for as long as an hour to refresh the screen. If I looked at the Task Manager, CIV was taking up 97-100% of my CPU time.
When I upgraded, I tested some of my 'slow' games, and turns that used to take an hour completed within a minute.
I can still FORCE my CIV turns to take a long time if I have a large number of automated workers and I have all the automations turned on (a 'long gime' now being as much as 10 minutes, compared to an hour or more on my old computer). But if I FORCE the slowdown, the Task Manager shows only about 50% of the CPU being used by CIV (Conquests). So. on my system, the graphics is the bottleneck - it's not the CPU.
(FYI, the 'slow' game on my new computer was a standard sized map with close to 100 cities and around 70 automated workers.)
Try turning off the animations, turn off the options to show your own automated or manual moves, and hold down the shift key while your friends and enemies are moving.
(My 'old' computer had a Celeron processor - don't remember the speed - and 512 Mb memory.
Also, with my new computer, when I was testing the 'slow down' complaint about running Civ and a utility program at the same time, when my game sizes (# of cities, # of workers, map size, animations on, etc) when I'd get near the point when I'd get black screens, it might take up to a minute of time between the time my last automated worker moved until the system told me to 'press enter', so I assumed I was CPU bound, not graphics bound)