re: Aspen, CO in Summer?

Raft the Colorado River, it's not too far from Aspen.

Or you can raft the Arkansas river and take the beautiful Independence Pass to get over there. Also not too far of a drive. You'd want to do the upper sections like Numbers or Brown's canyon.

Definitely do a full day trip no matter what river and section you end up rafting. Full day is usually from 8-4ish with a riverside lunch stop. It also depends on flow and wind that day. Some days you'll cruise through your section, other days it'll be slower going.
Hiking around Maroon Bells is must, but you won't be alone by any means unless you start getting way back up towards the passes around the bells (it's known as the 4 pass loop around the bells).

Biking, fishing, ATVing, hiking, drinking, etc are all nearby and plentiful.

Hanging Lake is a really cool spot that's easy to get to and back in a day's trip from Aspen.

Enjoy!