Boulder was, long ago, a place where advanced scientific research took place. The University of Colorado, IBM, and Ball Aerospace were located here. Supported by money from Denver's industry and an active military presence, Boulder scientists made advances in medicine (bio-med gel was invented here), alternate energy sources, robotics, and even developed a power armor prototype. Unfortunately, leakage from the Rocky Mountain Arsenal (a nearby toxic waste dump/weapons storage location) caused a poisonous cloud that killed a lot of people in Denver. As an apology, the military funded a program to create a self-sustaining research dome, capable of withstanding a nuclear attack. This "city of the future" was to be a prototype for settlements on the moon and other planets.
Then the war with China began. The USA annexed Canada. Boulder became a hotbed of political activity, as most of the scientists were naturally suspect of the military, and they, their families, and friends staged public protests about the situation, which got much of the city population up in arms. Some of the protests turned into riots, and the riot police were called in to suppress the riots. That squelched it but left everyone at a low simmer. When reports of plague outbreaks in Denver surfaced, many in Boulder feared that an exodus from that city would come here and infect them; they fled north. When the bombs fell, Cheyenne Mountain (a military facility, home of NORAD) was a primary target. A huge section of the mountains became a great radioactive smoking crater. Coupled with attacks on Denver and the Rocky Mountain Arsenal, Boulder became the center of a triangle of hellish death.
All along the front range of the Rocky Mountains, city after city was cratered from the nuclear weapons; it seems China really wanted Colorado out of the picture. Boulder was no exception, the surface city turned into an ashen wasteland. Only a few buildings were left standing in town. Yet, atop its little hill, the massive Boulder Dome still stands strong.
Outside, Jackals roam around the city, preying on animals and humans alike. Glowing ghouls also inhabit the area, having come from Denver in search of supplies. Inside, with post-war dangers lurking everywhere, the scientists use the Dome as their sanctuary, quarantined until they find a cure for the plague. It's not like they have a choice to abandon the Dome anyway; after all, ZAX is in dire need of new memory storage, and he is the only reason the Dome stays functional.
The Boulder Dome did not appear nor was mentioned in any published games, but was going to appear in Van Buren, the canceled Fallout 3 by Black Isle Studios. It is not certain if it will appear in any future Fallout game.