There are some fabulous roads in the Sandhills of Nebraska - truly top notch.
I suggest traffic volume maps from the various states from their DOTs.
ND - http://www.dot.nd.gov/road-map/pdf/traffic/trafficstate_2013.pdf
SD - http://www.sddot.com/transportation/highways/traffic/docs/Traffic_2013.pdf
NE - http://www.transportation.nebraska.gov/maps/Statewide%20Traffic%20Flow%20Maps/2012-Statewide-Traffic-Flow-Map.pdf
CO - http://dtdapps.coloradodot.info/staticdata/Downloads/TrafficVolumeMaps/TVMap1.pdf
Nebraska also has a nice cycling map -
Diagonal roads are rare in the Great Plains -
And when they do exist, they often attract high traffic levels.
There is a core route section from Valentine, NE to Sterling, CO that you should strongly consider.
From Valentine -
NE 97 south to Tryon
NE 92 west to Arthur
NE 61 south to Ogallala
US 30 west to Big Springs
US 138 - west to Sterling
This route has extremely low traffic, small towns at intervals, and great scenery.
Be aware that early summer is far better than mid summer when it can be brutally hot.
From Sterling into Denver you can follow US 6 and service roads -
But it gets increasingly tricky as you approach Denver metro.
In the eastern Dakotas you have a range of roads to choose from -
Generally they form a grid - so you will be going south, then west.
From the traffic maps above you can select highways with low traffic.
Best - J