Oh man, what an opportunity!
Leave Vegas (as quickly as possible!) and head for Zion National Park (Hwy. 9.) From Zion, head east to Carmel Junction and pick up Hwy. 89 north to Hwy. 12, one of the most spectacular roads in the United States. Head east on Hwy. 12 through Red Canyon and Bryce Canyon - Bryce is just a short side trip from Hwy. 12. You don't want to miss that.
After Bryce, continue on east on Hwy. 12 through Escalante and Boulder on the way to Hwy. 24, which will take you on through Capital Reef National Park. From Capital Reef, keep heading east on Hwy. 24 to Hanksville, then head south on Hwy. 95 through some spectacular red rock canyon country, crossing Lake Powell along the way, just below Cataract Canyon. Hwy. 95 will take you by Natural Bridges National Monument (worth a visit) before intersecting with Hwy. 191 south of Blanding, Utah. From there, head north on Hwy. 191. You may want to ride on up to Moab and take in Canyonlands and Arches National Park, or you can turn eastward again at Monticello on Hwy. 491. Hwy. 491 will take you on into Colorado, passing through some terrific mountains and canyon country along the way.
Follow Hwy. 491 until you reach the intersection with Hwy. 160 in Cortez. Stay on Hwy. 160 until you reach Durango and then head north on Hwy. 550.
Follow 550 to Montrose and then turn east again on Hwy. 50 to Poncha Springs. At Poncha Srpings, head north on Hwy. 285. You can then choose between the 'short' route to Denver across Hwy. 285, or head on north on either Hwy. 24 or Hwy. 91 to pick up Interstate 70 east of Denver.
The riders that are more familiar with Colorado will probably be able to suggest some great lesser-traveled roads than the ones that I suggested, but having driven those a few times, I have to say that I can't wait to hit 'em on my bike. As for Utah, I've driven most of the roads in that state and can't think of any route that beats the one I mentioned for the time frame that you have. I didn't include any dirt roads, but there are some great ones in both states if you're so inclined.
Best of luck and I hope that it's the trip of a lifetime for you!
Oh yeah, one thing to be really aware of is the large amount of wildlife on the roads in both states. Be especially wary within a few hours of both dusk and dawn.
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Don't you think that it's a ^%#$&# shame that Hunter S. Thompson wasn't an adventure rider? Imagine the ride reports...!