You are going to have a great trip. Hope you are allowing for plenty of time to see the sites.
We have made several similar trips and just our opinion it gets really boring across some of the Midwestern states. We head up across Iowa to avoid the St Louis traffic and have a couple of places we overnight on I-80. You can save several miles if you use I-680 instead of heading toward Omaha to head north on I-29. In S Dakota on I-90 there is a Cabelas in Mitchell that invites RVs to come in and spend the night in their lot. Then just set sail toward Rapid and the Hills. So much to do there that we suggest you do a google search on activities and attractions in the Black Hills. Lots of places to stay.
Maybe stop at Sundance Wyoming and see Devils Tower. Stop at Little BigHorn Battlefield and pay respects to all the soldiers who were killed there. There is a great history museum with a lot of artifacts and photos. Visit Last Stand Hill there and see the actual locations these men, including Custer were found at.
You can approach W Yellowstone from several directions, but the easiest and still a beautiful ride, is to run I-90 to Bozeman and then 191 down to W Yellowstone. Most of that route is beside a river as it cuts through to the park.
From the park to GC is quite a drive and there are any number of side trips and things to do. We love the Wind River Canyon area, although that route will lead you just a bit east from due South to the canyon area.
I write too much and too long! Have a great trip and take your time to enjoy it all
horsedoc
2008 Damon Essence
2013 Jeep Sahara Unlimited
Blue Ox tow