The tallest building in Kentucky is Louisville's AEGON Center, designed by Philip Johnson and John Burgee, the architects who brought the world the Puerto de Europa, the PPG Place in Pittsburgh, the Crystal Cathedral of Garden Grove, and the infamous Lipstick Building at NYC's even more infamous corner of 53rd and 3rd.
According to Wikipedia, "the building is constructed of reinforced concrete, as opposed to the steel construction usual for buildings of its height." Interesting. You may make of that what you will. It was completed in 1993, and has held up just fine since then.
Although you can't see it in the close-up photo above, there is a way to get the absolute top of the building by way of a secured ladder-tower leading from the center of the dome's interior, going up to the pinnacle.
There's a photograph of it here on the official U.S. Coast Guard flickr site. I'd love to get up there and take some photos myself.
