Sspeed - Nebraska has some of the finest touring in the Great Plains. I have traversed the state many times - including on my very first cross-country trip. I think crossing Nebraska is way more scenic than Hwy 96 in Kansas. That said, spring is a very stormy time - not to mention there's a big difference between early spring and late spring.
Anyhoo, leaving from Denver is rather tricky. There is no longer a good back road from Denver to Fort Morgan. I-76 was built in many places right over US 6. Sometimes there is a butt-ugly service road right up against the interstate - other times you have to ride on the interstate - legal but not pretty. I suggest hopping on a shuttle bus and riding from Fort Collins east on Hwy 14. Way nicer.
From Sterling, you can follow the South Platte valley up to Julesburg on the old road - US 138 - almost no traffic.
Nebraska presents a number of opportunities depending on your preferences. US 30 follows the Platte Valley and has moderate-plus traffic, but good shoulders for the most part and lots of towns with services. But, but, but - - Hwy 92 from Arthur to Broken Bow runs thru the Sandhills - an area where the land has never been plowed for farming. There is almost no traffic and you can see what the Great Plains looked like 200 years ago.
From Broken Bow you can continue eastwards on Hwy 92 (I'm assuming you will see the advantages of choice #2 above) towards Omaha with increasing traffic. Or you can continue northeast on Round Valley Road to Sargent. Then head east on Hwy 91 and zig northeast thru Norfolk and Wayne, a college town.
Here is a traffic volume map of Nebraska - http://www.nebraskatransportation.org/maps/Statewide%20Traffic%20Flow%20Maps/2010-Statewide-Traffic-Flow-Map.pdf
Which I think is better than their Bike Map - http://www.transportation.nebraska.gov/docs/bicycle-guide-current-2.pdf
Small towns in Nebraska are usually very generous to cyclists - letting them camp in town parks when they don't already have a small campground. By all means, explore Nebraska.
Best - J