The Kiddos, the Mountains, but where..?

“Hey all,
So I'm planning to get my two boys--8 and 10-- into the mountains for a week of backcountry hiking, camping, loafing. We're shooting for the Rockies, CO or MT.
Problem is, I've spent most of my hiking time in Utah canyon country and don't know good spots in the Rockies for a scenic, mild adventure the kids could handle. I'm thinking just a couple miles a day, at most, or a slightly longer hike to a base camp where we could do day hikes from.
Would like to avoid the crowds at the big national parks.
Anybody got ideas? Favorite family backcountry spots?
Many thanks.”

“Birch and I honeymooned at Pike National Forest, Gibson Lake. It was a simple hike up, along a stream. Stopped up top, next to an alpine lake, and hike where ever from there. The bugs were awful out of the treeline...but that was also twelve years ago. We saw two people the entire time we were there, and that was on the way out.”