Tom,
From Longmont heading ENE, there are not a lot of great bicycling roads. If you don't mind riding on Interstates, you could ride east to Hudson (via Weld County Roads 6, 27 and 8 ), and then follow I-76 into Nebraska. Bycycles are allowed on this portion of I-76. One advantage to I-76 is regular access to services (which is not something you can say about a lot of other roads in Eastern Colorado).
If you're willing to deviate south a bit, you can ride on US36 (via Hudson, Prospect Valley and Bennett). US36 is a high-speed major highway, but it doesn't get that much traffic because most people heading east prefer I-70. US36 has a shoulder the whole way, but carry a lot of food and water because services are scarce (there's a reason a "town" named "Last Chance" is on this highway). You can stay on US36 all the across Kansas and Missouri if you want.
If you're willing to deviate farther south, you could follow the TransAm through Ordway and Eads. This would have the advantage of having the great ACA maps to follow. In fact, you could follow the TA all the way through Missouri before heading north.
A copy of the Colorado Bicycle Map can be acquired from the Colorado DOT, which would show you many other alternatives. This map tells you how much shoulder each road has, and whether or not bicycles are allowed. Be careful following roads you might find on Google Maps in eastern Colorado, as many of those roads are unpaved.
By the way, Longmont has some great bike paths. You also might want to pick up the ACA Great Parks South map #1 for help getting from Steamboat Springs to Longmont.
