Yes, the Yampa is on the Western slope of the Rockies and does flow west. The section that flows through Dinosaur National Monument is lottery-permitted. That is, you need a permit to run and the lottery is closed for the season. If you want to float Dinosaur, you might try finding a group with open seats. As for having trouble with a canoe, if you don't have experience on big class III-IV water you will be earning your wings so to speak. You might want to consider hooking up with a professionally guided tour for your first run at a river like this.