If you're staying downtown and want to run from the hotel you should take Bijou street West (towards the mountains) and across Monument creek. Once there, you can either
A) hop on the trail and run North to Monument valley park (a mile or so) where there are a few nice trails, or if you want a longer run keep following it north until it turns back to dirt in about 8 miles when you have gotten to the AFA grounds
OR
B) run south on the trail, follow it underneath the interstate and past the wal-mart and into Bear Creek Regional Park where there are a shit-ton of trails (cross 21st street to the west) that could ultimately lead you up into the mountains (gold camp road, high drive, section 16, intemann trail, etc) depending on how long you want to run.
Or, if you want to drive to a run, i would suggest either waldo canyon, gold camp road, or section 16. both waldo and sect. 16 are 6-7 mile mountain loops and gold camp is a dirt road that goes on forever back up into the mountains (40ish miles to cripple creek).
if you want a sweet-ass long run drive up to rampart reservoir and run the 14-15ish mile loop around that. GORGEOUS singletrack at 9000' without much climbing to speak of.
Or, just run in the Garden. Great trails there, too.