Awesome thread, kyoto. You're actually sorta right. First the Pittsburgh part, a LOT of people from PA consider it an east coast state, even though it has no real coastline or beaches on the Atlantic. So Pittsburgh is basically as East Coast as Philly is. And Pittsburgh used to be considered the western frontier for a long, long time. These things are not set in stone, they're fluid with the movement of people and culture. Kansas was the western frontier at one point, too, and actually still has a lot of that western plains feel, like Nebraska and Oklahoma and the Dakotas. It didn't stop with the end of train robberies. You might find more people agreeing that those are all western states on the high plains than you will that Denver and the Front Range are midwestern. That doesn't mean there's no truth to the latter, these are not absolute nore mutually exclusive distinctions.
Now for Denver, as others have pointed out it has maybe more in common with San Diego or Sacramento than it does with Durango, Pueblo, or even Colorado Springs. Go to a baseball game at Coors Field in LoDo and from your immediate surroundings going to and from the stadium you feel way more like you're in downtown Lincoln or KC than in downtown Leadville or Steamboat. Being able to see mountains from within city limits doesn't make it a mountain town, necessarily. Ask anyone who's lived a long time in Alamosa, Gunnison, Montrose, Glenwood if they consider Denver to be a mountain city. You'll probably get laughed at. People in mountain towns look at the Front Range as little more than where the major airports are and where the affluent recreational skiers almost exclusively reside. Sure, there's a big difference between western and mountain, but this is simply analogous. Denver grew and prospered because it was located on the plains, not the mountains or even the foothills, and could serve well as a supply depot for mining industry up in the mountains. Same for Boulder and other Front Range cities. Wyoming has amazing mountain ranges in it, too, but nobody would consider Cheyenne or Laramie to be anything but midwestern flavor plains cities.
While some of the earliest leaders were East Coast hucksters, Denver was originally founded and settled primarily by midwestern types (look up the name Larimer, for starters). Same for Boulder, Greeley, and Ft. Collins. That flavor took root and has maintained. Outside of Chicago, you probably won't find more transplants from Ohio, Indiana, Wisconsin, Iowa, Illinois, Michigan, Minnesota (i.e. midwestern states that don't share a border with CO) in one place combined than in Denver. They bring their midwestern ways with them, even if they came looking for things that are distinctly different. Once CA residents started arriving in waves, their west coast ways came right along with them even if they didn't have a beach to ride a cruiser bike down to. Denver became more liberalized with so much brain drain from these other midwestern states coupled with the Cali influx. Denver wasn't always liberal, Boulder was pretty conservative too until the government labs opened in the 1950's. Nobody's publicly assembling to protest WalMart stores in Littleton, Aurora, Golden, or Castle Rock. In fact, city leaders in Denver were hoping to lure the Amazon 2.0 campus. The eastern half of the state retains the conservative feel that it once shared strongly with Denver for a long, long time. You know that as recently as 1972, not a terribly long time ago even if it was before most on this board were born, Colorado citizens used the initiative process to reject the already-awarded 1976 winter Olympics? Conservative NIMBYism still calls the shots, even in crunchy, hippy Boulder. Things change and Denver metro today probably has more in common with the Inland Empire than it does much anywhere else.