I have done this trip from where we live in East TN and I took I-40 to Nashville and picked up I-24 to Paducah KY and then cut across on secondary roads Rt. 62/286 to Wickliffe and take the bridge over the river into Cairo, stay on 62 all the way over to I-55 at Sikeston MO. The bypass around St. Louis is not bad at all but time of day does make a difference traffic wise. I picked up I-70 to Kansas City, again the bypass is good, then pick up I-29 to Sioux Falls an then I-90..the rest is cruise on into Rapid City. I would do this route again if we ever head that way in the future. Have fun.