I'm not normally a huge fan of faux historic architecture, but that Nashville tower is badass. I also really like the new museum wing in Houston. It looks like it's created some cool spaces to exhibit art in.
For Los Angeles, my favorite building constructed this century is probably the Wilshire Grand, though the Lucas Museum could be a contender once it's finished. The devil will be in the details with that one, but it could be a real show stopper if it matches the renderings.
For Cincinnati, it has to be the Zaha Hadid designed Contemporary Arts Center (2003). It's Hadid's first American building, and the first American museum building designed by a woman. It's striking at street level, and its contemporary design stands in stark contrast to its surroundings, but the interior spaces are really where the building shines. Stairs appear to float from floor to floor, galleries can be completely rearranged for different shows, and there's a porosity to the building that makes the interior feel seamlessly integrated with the outside downtown environment. It's a must visit if you're in Cincinnati!