I have driven it across Nebraska, to Shoshoni, Wyoming, and across Idaho from where it picks up out of Idaho Falls.
There is no more relaxing way to cross these three states and none more scenic!
Enjoy, U.S. 20 is a great, great drive.
As I remember, US 20 in Wyoming passes through Casper, Thermopolis, Cody and then through Yellowstone's East entrance and out the West entrance at West Yellowstone. The road through the park is usually closed from early-mid November until Mid-April. I beleave most of it through Wyoming is still 2 lane. Great scenery and lots of interesting places to visit. You will have a great trip.
East of the Mississippi there are a few long stretches of urban and suburban stop and go: 30 miles through Cleveland, 40-50 miles around bottom of Lake Michigan to the western edge of metro Chicago. Lesser slow spots include Buffalo and Toledo, you go into the city center on surface streets, then back out.
After Chicago, the drive is great, at least to Nebraska, about as far as I've followed it. Plan to stop for at least half a day in Galena, Illinois.
I agree about Galena. Great shopping district and interesting history. Take a guided city bus tour to learn more about the interesting history. Then stop in Dubuque and visit the downtown Museum of the Mississippi River. Then if you have time visit Eagle Point Park for some great river views.
A little farther west is Dyersville Iowa where you can visit there Ertl Toy Museum and the always popular movie site where Field of Dreams was shot.
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US 20 takes you right downtown Cleveland. Lots of stop & go through the eastern suburbs. Mostly four lane with some three lane. An intersting trip. Have fun!!
Indiana is OK after you get about 20 mile East of the Illinois line. Ohio is great until you reach Toledo. It can be done, but watch the time of day that you travel Toledo and Cleveland. I would bypass Chicago, Toledo, and Cleveland.