psurich wrote:
Our journey starts about 30 miles north of Wichita.
How much time do you have and what kinds of things do you want to see along the way. You could take I-135 to US-81 to I-80. Along I-80, there is the 
Great Platte River Archway and Museum, 
Fort Kearny, and the original Cabela's in Sidney, NE which even has a campground.
If you were to take US-26 West from Ogallala, NE; there is 
Scotts Bluff National Monument, 
Fort Laramie National Historic Site,  
Guernsey State Park, 
Register Cliff and 
Oregan Trail Ruts.
I-25 will take you to Casper and then US-20 will take you to Thermopolis where there is 
Hot Springs State Park, 
the Wyoming Dinosaur Center, and 
the Legend Rock Petroglyph Site.
From Thermopolis, WY-120 will take you to Cody where there is the 
Buffalo Bill Center, 
Old Trail Town and the 
Nightly Rodeo. A loop of the 
Chief Joseph Scenic Byway and 
Beartooth Highway with a stop in Red Lodge makes a nice day trip from Cody.
From Cody it is a pleasant, scenic but sometimes slow drive through the park to West Yellowstone.
I also recommend stopping in the Tetons as mentioned by several others. You could go one way and come back the other.