I live in Broomfield, which is about 20 mins drive to the NCAR trailhead (in Boulder. From there, I hop on the Mesa trail over to Chataqua Park (and more trails), Bear Peak, Green Mountain, Flagstaff, Eldorado Canyon and Flatirons Vista Trailhead off Hwy 93. You have many options and many miles of trails, depending on how far and which way you want to go, whether you want milder trails or more technical trails with elevation gain.
I have noticed that, over the years, many trail runners (in Boulder, particularly) have gotten more serious and a lot less friendly... almost as if they have to size you up rather than say hello. I still smile and nod or say hello anyway... even if I am out of breath. Also, I try to stick to the trails during the week since they are less busy. It makes everyone happier, even though I go out of my way to be polite and give right-of-way. Overall, the culture of Boulder has changed over the years - from a casual, sort of bohemian society to a more upper-class. The city is beautiful, with the backdrop of the Flatirons, and has a wonderful energy.
You can find races (from 6 miles to 100 miles) on active.com, runuphillracing.com, or in Trail Runner magazine (or TR mag online), for trail races along the front range or in any of the mountain towns.
You'll love living in Colorado and the many options of trails and races! Make sure you check out the Jefferson County Open Space trails west of Denver/Golden.
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TrailChick5