I have made the the trip to Yellowstone many times from near Detroit Lakes MN to Yellowstone via I94. From St Paul I would recommend Ft Abraham Lincoln state park near Mandan ND, 701-667-6340, or the Medora Campground & RV Park, 701.623-4435. I would recommend reservations for both if you are traveling on the weekend.
Makoshika state park at Glendive MT is another possibility. Again you should have reservations on the weekend.
My preferred route with a motor home to Yellowstone is I94/I90 to Laurel MT then South to Cody WY via Belfry MT. Near Cody you can take Dead Indian Pass to the NE entrance via Cooke City MT or use the East entrance via Cody WY.
Enjoy your trip
