With all the people in your travel group, I would not want to be changing hotels too many times.

I also would not suggest CO Springs (not a mountain town) or the Air Force Academy (I can see the teens yawning now!).
I suggest you focus on the Colorado outdoors and activities, per your OP.

Again, I recommend Aspen, with maybe a stop on the way there and back, like in Georgetown, Vail, Glenwood Springs for lunch or an overnight.

Drive another route back to Denver from Aspen, over incredible Independence Pass.

Fly in and out of Denver. Stay the first night in Boulder, if you want to acclimate. It is a cool town, and HS grads might be interested in seeing the gorgeous campus. We have toured many, many campuses, and we think CU-Boulder is tops for setting and architecture.

Aspen is beautiful, and it is a special place to visit for a special graduation trip. Go to their website to see what events are happening. They have lots of outdoor music festivals, for example.

Look what's happening in Aspen in June, for the adults in your group:

JUNE
Jun 14 - 16 FOOD & WINE Classic in Aspen

Spent a week West of Denver last summer. Not an expert but If I was younger I know one thing I would have done. Between Blackhawk and Boulder looked like a happening place. Tubing, cycling and hiking with tons of young people everywhere. Try hwy 119 west of Boulder.