Hunters in Colorado take a lot of elk during the over-the-counter 2nd and 3rd rifle seasons every year. You still have some good options out there. A couple words of warning, though: The OTC seasons in CO get some pressure. You'll want to get away from roads if you seriously want to get into the elk. I always suggest that guys coming from out-of-state, at the very minimum, nail down someone who can remove meat from the field with horses. Colorado backcountry is very high. Killing an elk 4 miles from the nearest road is an awesome experience, but the work can be daunting when you figure that you have 300 lbs of meat and 4 miles back to the truck at elevations that are 2 miles above home.
Don't let that discourage you, though. CO has some great country to hunt. Find a place that holds elk that puts some distance between you and the bulk of the hunters. (There are options all over the western half of the state.) Then find an outfitter or someone with horses who can drop a camp for you or at least come get your elk should you harvest one. If you choose not to camp in the backcountry but instead at a Forest Service campground or a drive-able campsite, expect to put some boot leather down in the mornings.
They are bigger and prettier than those other elk. 
