When will you be here and what is it you want to do?
CO is a big state. Where will you be going? Are you camping or staying in a city/town? Fishing? Other activities?
Trail Damage is a good place to start. The Charles Wells books are also good guides.
For someone who is relatively inexperienced and looking for great scenic trails, I could recommend quite a few (you can find links to all of these at Traildamage):
Near Denver, I would recommende these for a relative beginner:
* Mosquito Pass (between Leadville and Alma)
* Saints John/Deer Creek (summit County area)
* North or Middle Fork of the Swan River (Saints John connects with these trails.) (Summit County area)
* Kingston Peak (Northwest of Blackhawk/Central City)
In the San Juans, SW corner of the state, I'd go with
* Cinnamon Pass
* Engineer Pass (these two trails run parallell to each other, both run between Silverton and Lake City, so a typical run is to do the "Alpine Loop", starting at either end and running both trails, ending up back where you started.)
Keep in mind that the "4 wheeling season" in Colorado starts much later than you might think. Many trails are still closed in late June so if you are planning on hitting some of the higher trails (all of the ones I named above) figure on early July at the soonest. FWIW, there are some years when Mosquito Pass, for example, NEVER opens because of snow (I've been blocked by snow on Mosquito Pass in mid-August.)