In order to drive on every road that is not paved, you had better buy a Jeep instead of renting one! I have crawled all over those mountains since I can remember, and I STILL have not wheeled all of it!
I hesitate to give you reasons to visit Colorado, because once you have been here you will probably want to move out to Gods Country. We love tourists and their $$ but don't need more residents. Just kidding, sorta, there is just too much to mention as you might gather from the previous posts. Just pick out a few things to do or see, else you may wind up spending all your time in Colorado. Consider climbing one of our 14,000' Mountains. Many are not technical climbs and the views from on top are incredible. Visit http://www.14ers.com for trail info.