We spent a week this past summer at the Garden of the Gods campground in town. While the AT&T cell service was not good at that location and the Wifi was questionable at times (most of the time) we enjoyed the stay. We spent very little time at the campground and the central location was great.
My favorite place to stay without our RV is the Broadmoor Hotel where I have spent a week or so at different times, back when I had an expense account. LOL Nice doesn't begin to describe the Broadmoor. Mr. Penrose did himself and the community proud when he built that facility.
Many forum members like the Cheyenne Mountain State Park but I have never been able to get a site there in the summer. Need to plan ahead more I guess. The KOA in the south part of town is also acceptable as we spent a couple of nights there a few years back just passing through town. (my wife grew up in the Springs and in Woodland) We tend to stop there most summers for a few nights.