The Colorado Capital has a tour that runs every business day. It is an interesting tour that is free and talks a little bit about Colorado history.
As a resident of Colorado, I accompanied some guests to see the place. I came back pretty amazed as there was plenty of information to hold my interest.
The dome is probably the best part. I enjoyed being able to look out to the Rockies and see the mountain tops as well as the area as far as the eye can see.
This is a heavy duty walking tour, so do be careful if you have trouble walking or if the kids tire easily. There were two sets of stairs (one next to the murals on the walls), and they can kill you with the wrong shoes.
Make sure (even if you don't check out the tour) to look around at the Capitol. On the steps out front you can see the interesting cap indicating the mile high issue above sea level. A must-see for the first time Denver visitor, but recommended for the resident as well.