Eldorado Canyon, (directly) outside of Boulder, is one of the bastions of Colorado trad. Some excellent climbing here, with easy approaches. A great route to start on might be the Bastille Crack.
Lumpy Ridge is a little bit of a drive from Denver (1 - 1.5 hrs), but also has reasonable approaches. Directly outside of Estes Park. Excellent quality rock, & great views to boot. Fairly stout ratings.
Right up the road from Lumpy is Rocky Mountain National Park, of the alpine rock capitols of the lower 48. Great climbs, good to excellent rock, & phenomenal views.
Clear Creek Canyon has a good mixture of sport & trad lines, good rock, & an easy approach. Less than a half hour's drive from Denver.
The Colorado Rock Climbing Falcon guide by Green, while just an overview, is actually quite good, & gives an excellent overview of the climbing possibilities throughout the state- highly recommended.
Hope this helps. Have fun!