Mountain Dale is very nice. We've been there several times. North side is mostly full time residents and the south side is used for actual campers. Its a good base for going to Canon City, Royal Gorge and Colorado Springs. Its about half way between them.
Also Mueller State Park is good for Elk, but in the fall it can be cool as the park is at 9000 ft. You might even get some snow.
North of there there is Golden Gate Canyon State Park - also high (8,000 ft).
One other spot that may not be open in late fall is Brainerd Lake Recreation Area - its even higher at 10,500 ft and generally closes in mid October. You want a site in the west loop. The east loop had a micro burst a few winters ago that knocked down all of the trees.
All these locations are popular and you will need reservations, especially for weekends.