Start in Georgetown, CO. Cycle over Guanella Pass (11,669) to Grant. Head southwest through Jefferson and on toward Hwy 9. Then take Hwy 9 south through Breckenridge and out over Hoosier Pass (11,541). Continue on through fairplay and take 285 to 24 up to Leadville, the highest city in the U.S. Continue on 24 through Minturn to Vail and then turn east to cycle over Vail Pass (10,554) [there is an awesome dedicated bike path here running all the way to Frisco. The run through the canyon down from Copper Mountain is incredible]. Wind up in Frisco, ride around the lake to Keystone. Ride up through keystone toward Montezuma and (walk/scramble/push/hike/climb/freak-out) over Argentine Pass (13,200) and ride down the other side back to Georgetown. About 80/20 on road/off road I think.

It isn't the most passes you can cram into a week, but they are some of the prettiest and highest. The view from the top of Guanella is amazing, especially looking east toward the front range and Mount Evans, and the view from the top of Argentine is like being on another planet. The stars come out before the sun sets sometimes up there, and the wide expanse of the Peru Creek drainage is awe inspiring. Watch out though, I know you said paved/unpaved didn't matter, but that's really mountain goat territory.

Also, check on the status of Guanella Pass. There was some talk about closing it due to a rockfall situation, and I stopped following it a year or so back.

Someone else may be able to fill you in on the passes in the more southern parts of the state. I haven't ridden them personally, but I have traveled there numerous times, and highly recommend looking into the areas around Durango, Telluride, and Ouray. Monarch Pass and Crested Butte are amazing as well. There's just too much beauty in Colorado to try to narrow it down... it's hard.