If you're driving from KY you'll likely be going through SD. My wife and I mildly enjoyed the Badlands, Mt. Rushmore (my wife was more impressed than I was) and Custer State Park on the way to Yellowstone.
Google may send you up through MT but it's better to go through Sheridan, WY from western South Dakota and head straight west through the Big Horn Mts to Cody. The Buffalo Bill Museum in Cody is pretty cool.
I have seen a lot of the national parks. Yellowstone is the first and the best. It doesn't take very long to see it, just a couple days if you only hit the main sites but of course you might want to stay a few days for hiking, fishing, wildlife viewing, exploring, ranger programs, etc. We saw grizzlies, black bears and bighorn sheep right on the road, all kinds of elk and deer, lots of buffalo and antelope galore on the way there.
Like a lot of folks, we stayed in West Yellowstone for the lower prices. Its an easy drive into the Park. It is getting really late to book inside the park and it is expensive. Most park events and even stuff in Cody start June 1 and end Aug 31. We went the last week of May and some things were not up and running.
If you've got the time, I would drive back by going south out of the park through the magnificent Tetons, then through Rawlins and down through Saratoga and Walden, CO back through Denver and take 70 East. It definitely takes more time but it's awfully nice.
Otherwise, the drive from NW Wyoming angling SE through Wyoming is really dull and eastern Colorado or western Nebraska are sure not much to see either. If you don't take the longer way back through Colorado I would just go back the way you came through South Dakota.