Tom,
Here are some routes I did about 5 years ago. I re-created the routes on RWGPS based on my notes. Take them for what it is worth. Where specifically are you going in Nebraska? Do you want/need to go to Cheyenne or what?
This route was not the most memorable trip for me (it was part of a longer trip and was more of a connector type route) and I don't recommend it as a "enjoyable" trip, i.e. miles not smiles type.
A couple of notes on the routes. As I said, these are 5-6 years old. The traffic & services then may not be what it is now. Then they were fine. I am pretty sure a few extra miles of bike paths are available now (which I included on the RWGPS) compared to what I had. I was coming from southeast of Denver so never got to Denver. If you can start from the airport, it is easy to get to the route by heading south from the airport on Jackson Gap Rd. then east on 60th Ave. to Imboden Rd. where you would join the HCWC route, which does have about 1-2 miles of gravel. To get to the airport from downtown Denver, take the light rail, bikes are allowed. Anyway, there was a campground in Hudson. I got a hotel in Fort Collins. I did have to ride on the actual interstate for about 15+ miles but it was OK. It was the wind that was a pain at times. I didn't have direct headwinds but even the angled headwinds were quite strong. Sorry for the multiple routes. I just piece together various routes (I have thousands) to create one. While there is a frontage road most of the way, it is gravel for those 15 miles I rode on the interstate. Here are the routes, hope it helps:
https://ridewithgps.com/routes/36142062
https://ridewithgps.com/routes/36141838
https://ridewithgps.com/routes/36141940
https://ridewithgps.com/routes/36142211
https://ridewithgps.com/routes/36142349
Tailwinds, John