There are many, many great places to take the family camping in Colorado. Most, however, are an hour or more from the Front Range cities of Denver, Colorado Springs, Pueblo and the smaller towns north of Denver. It is definitely worth the effort - it just takes some planning.
My husband and I prefer primitive rather than organized camping, but several times we have visited U.S. Forest Service campgrounds and thoroughly enjoyed it. On one occasion, we just packed up our truck and headed west out of Colorado Springs on Highway 24. We just kept driving until we came to Highway 285 and turned south. Now there are many small (usually unpaved) roads off Highway 285 - so we just picked one.
What we found was a site with about 10 spaces and no people! Wow! We really lucked out! We actually found a place to go camping in Colorado away from the crowds - and it was a weekend too!
During our stay the only visitors to the entire area were the permanent residents, the forest creatures.
The Gray Jays were plentiful. Their boldness has earned them the nickname of "camp robbers".
They zoom in for a table landing right while you're eating and steal any food they can get away with.

The Blue Jays are a bit more shy. They prefer to be coaxed into taking a piece of food.
Then there are the squirrels. One of them took a liking to my husband and ran right up his pant leg while being chased by another squirrel. Upon realizing that the human leg was NOT a tree, the squirrel promptly ran down and scurried off. Needless to say, my husband was quite stunned for a moment.
Since it was late fall, the leaves were turning vibrant colors of mostly yellow (Aspens) as well as some hues from Mother Nature's paint pallet of oranges, reds and pinks.
So the best time to avoid the camping crowds is late in the season. Just head out to Highway 285 some weekend with all your gear and meander up some of those dirt roads - just to see where they go. Maybe you'll find a jewel of a spot like we did.
And you'll love the peace and quiet!