Given its geography, why did people settle in Denver? It doesn't seem to have any huge natural advantage from its location--it's not on a body of water, it wasn't part of the original trans-continental railroad, and it doesn't appear to be part of a choke point for trade.
The early years of Denver have a great deal in common with Fairbanks, Alaska, whose history I know in some detail. In both cases, a combination of transportation and continued mineral development allowed the cities to switch from pure boomtowns to established settlements.
In Denver's case, the initial Pike's Peak gold rush brought a flood of prospectors to the area. These in turn attracted businessmen to cater to the gold-seekers. Between 1858 and 1860, a series of small cities sprang up on and near Cherry Creek. These cities merged into Denver.
Now, the initial gold rush is a fascinating case: Not much gold was found until the second year. Had it taken longer to find, Denver (and its predecessors) might have ended up the victim of a "busted" rush, in the same way a lot of small towns did. Speculators were frequently attracted by rumors of gold, and if the rumors didn't pan out, they left.
In Denver's case, the rumors did pan out. They panned out to the point that Denver became a local hub for gold-seekers. The U.S. government established a post office, stores came in, and business flourished — to an extent.
If you track the census figures, you'll see that Denver's population stayed pretty much flat between 1860 and 1870 — right around 4,700-4,800 people. In reality, there was a significant dip (about 1/4) during the Civil War, and it rebounded with the coming of peace.
The next step in Denver's development came with the arrival of the railroads. Placer mining is light on equipment and doesn't require significant transportation. Hydraulic mining and hard rock mining, however, do require large amounts of equipment, and in the 19th century, this meant railroads were needed to transport equipment and waste rock.
Despite the wishes of city residents, the transcontinental railroad bypassed Denver and much of Colorado. City officials spent several years (and several failed attempts) to encourage outside investors to build a railroad to Denver. When those fell through, the Denver Pacific railroad was created with a significant amount of bonds purchased by Denver's own residents.
This railroad arrived in Denver on Aug. 22, 1870, and its effect can be seen in the census records. Between 1870 and 1880, Denver's population soared by almost 650 percent. Between 1880 and 1890, it more than doubled.
The reason is convenience. Denver had railroad access, and it was conveniently close to significant mining developments, such as Leadville. Regional hubs are critical for large-scale human development, and Denver was a convenient gateway between mining communities and the railroad networks that brought supplies.
By the end of the century, Denver was the hub of a spoke-like railroad network that extended across Colorado, which was enjoying a significant boom in metals.
Elliot West's The Contested Plains: Indians, Goldseekers, & the Rush to Colorado is a great source on this era of Colorado's history, and I'd also suggest Colorado Historical Society's Denver Inside and Out, particularly a paper in there entitled "Rails to the Rockies: How Denver Got Two Railroads (Sort of), but Not the One It Really Wanted," by Eric Clements.