it will take you a bit longer but so peaceful....... so relaxing. outside badlands of I-90 there is Spearfish and then just north a toen called Belle Fourche. Gas up ok. take 212 east and it comes out just again at I90 then get 212 again and it enters custer national forest and then right into Yellowstone. Lynn and i do it and even though it akes couple hours longer it so relaxing. one time we saw one car in 130 miles

bellefourche throug broadus past ashland then to I90 or cut down from garry owen but we never do. we go i90/ 212 south now to yellowstone. its a peaceful drive when you have time. and if in a hurry well i90 to sheridan and through. we hate it lol. look at a map. oh I mentioned you in a comment