Lots of choices for route, but an obvious one would be the
AdventureCycling TransAmerica trail. Getting from Denver to Silverthorne or Granby (both on the TransAm), would be a nice ride, no matter how you do it.
Lots of TransAm riders go down the Columbia River through Portland, instead of along the route in central Oregon. That leg along the Columbia is part of ACA's Lewis and Clark route. So, in essence, it's all laid out for you.
If you're looking for a bit more adventure and trailblazing, the state maps have great alternatives. For example, through the Sawtooth Mtns in Idaho, through the Wallowa Valley in Oregon...
If you take the TransAm route, three weeks sounds about right.
-- Mark