I don't have much to add that hasn't already been said, but my suggestions, if fine with renting a car, would be Golden, Idaho Springs, or Black Hawk. Golden would offer pretty close proximity to Red Rocks, not too far of a drive from the airport, and it feels like a mountain town despite it being within the Denver metro area. Idaho Springs is the closest actual mountain town that is pretty nice with enough in the town and surrounding area to keep you busy that I can think of. There are other towns closer, but none I would consider worth staying in. Black Hawk would be a little further out than the other two options, but it's pretty neat as it has some pretty decent casinos surrounded by mountains.
If not wanting to rent a car there are shuttles you can take from downtown Denver to red rocks. I would imagine most of these would leave from Union Station in the LoDo neighborhood, which you can take a train to from the airport.
Edit to add: traffic in can definitely suck, but parking surprisingly hasn't been that bad for me the few times I've been. If you're fine with getting there and hour or so before the show begins I wouldn't imagine you would have much trouble and you can tailgate.