Black Canyon of the Gunnison is cool (west), Sand Dunes National Monument(south) is interesting, and like others said before... Canon City (Royal Gorge), Garden of the Gods in Colorado Springs (I live within 5 miles of it! Neener neener!) and Rocky Mountain National Park (north) are all great.
I'm less familiar with the west, but Durango and Ouray (on the west side) are both really pretty. Southwestern Colorado (Mesa Verde) tends to be more interesting than northwestern (Dinosaur National Monument) in my opinion, but it depends on your interests. If you want to huff and puff, feel nauseated and want to pass out, you can drive to the top of Pikes Peak (The view at Will Rodgers Shrine in the Cheyenne Mountain Zoo is similar, in my opinion, but without the sickly effects).
For non-national-park attractions, there is The Denver Museum of Natural History, the awesome Denver Aquarium, and both the zoos in Colorado Springs (Cheyenne Mountain) and Denver have their strengths, and there is a little bug museum (The Mays Field Museum) between Canon City and Colorado Springs (just look for the giant bug on the west side of HW 115 as you get close to the Springs).
- Lime
PS: I still hate this forum software.