Good hiking in the mtns just west of Boulder. Closer to Denver, you might want to drive almost to the top of Mt Evans (> 14,000 ft elevation) and then a short hike to the top.
Please, please, please... if you do this, wait until your body has acclimated to the lack of oxygen. Or get a local to drive you.
I was in Denver for a two-week training course many years ago, and my boss offered me the company SUV for the weekend. The day after my arrival, I took off for the mountains on my own. As soon as I reached 10,000 feet of elevation, my brain began shutting down and I felt like I was going to pass out. I stopped the car, and tried to calm down and catch my breath. Nothing worked. I was able to find the "turnaround" lane to head back down. As soon as I was below 8,000 feet, I started feeling normal again. Scariest feeling of my life, especially since transport trucks were zipping by me on the left.
When I told my boss what happened, he said, "Oh, yeah...I guess I should have told you not to do that, so soon after arriving."
Moron. The speed of a vehicle doesn't allow your body time to adjust to the increasing lack of oxygen due to elevation gain, unless you've already been there for a couple of days.