Just a bit of a clarification on my previous response. I also agree that October can be a wonderful month to see Colorado, particularly if the timing can be last week of September, and first week or so of October.
My perspective in the previous response was from a USFS CG point of view. That's what my experiences have been the last few seasons. In 2017 we took a trip to the Grand Canyon, in late September and early October. Took US 285 to US 160 through Denver, Salida, Pagosa Springs and Durango. The colours were absolutely magnificent, right at their peak in many places. The drive was very pleasant, no real challenges.
We did notice that a goodly number of the USFS CGs that were accessible along those roads were already closed for the season, notably along US 160. But many of the commercial campgrounds/RV Parks were still open, and looked like they were still doing a good business. We had reservations in Durango going out to GCNP, and stayed in Mesa Verde at Morefield CG inside the park coming back, on their last week of operations.
If you want to consider areas further west, WEST of the Continental Divide, these and other areas already mentioned would be a good option.