State capital locations are often chosen for their geographical centrality or position near the state's center of population, offering a maximized number of people proximity to their seat of state government.

Another (historic) example of this would be Iowa. The first (1846) state capital was in Iowa City, which was far from being the state's most populace city at the time. However, at that time, the major population centers were primarily along the Mississippi River and the eastern parts of the state was much more thoroughly settled/farmed than the western parts. So, Iowa City was chosen as a logical point near the center of what was Iowa's population--giving people in all directions a pretty fair shot at proximity.

Shortly thereafter, the western parts of the state became increasingly/settled and farmed. So t adjust for this shifting distribution of population, Des Moines was chosen to be the state capital. Again, Des Moines was far from the most populace city at the time the capital was moved there. It did sit nearer to the center of the state's population though.

Today, Des Moines is recognized as Iowa's biggest city, though it didn't become so until about 1900. Dubuque was solidly Iowa's biggest city and economic powerhouse up until that point.

The same goes for Springfield, IL. It was the third or fourth(?) city to hold the state capital, all of which I belive had not been the state's largest city's at their respective times. Madison, Wisconsin was chosen for its centrality as well; it's pretty far South, I know, but it makes sense because northern Wisconsin is pretty sparsely populated and was even more sparsely populated at the time Madison was made. Lots of other states have similar stories too.