The Colorado State Capitol is the most recognisable building in Denver — a Corinthian dome plated with real 24-karat gold leaf, replaced periodically since the building opened in 1894. The gold was a nod to Colorado's mining boom, and the interior carries on the theme: walls of Beulah red marble (so rare that the world's entire supply was used here), white Yule marble floors, and brass railings.
Free guided tours run on weekdays and include the climb up to the dome's observation deck, where you get the best free panorama in Denver — downtown to the west, the Front Range stretching out behind it. The legislative chambers are also open when not in session. The building anchors the east end of the Civic Center, so you can easily combine a visit with the Denver Art Museum and the History Colorado Center.