My pick for a base camp location in Colorado would be Frisco.
It's a cozy little town, and it enables day rides in multiple directions.
Here's a RWGPS heat map of the Frisco area. Vail, Loveland Pass, Fairplay, and Leadville are are doable as out-and-back day rides.
My personal favorite in Frisco lodging is the
Hotel Frisco. Nice rooms and a great location.