HI we went to Yellowstone twice in the last 2 years. One of the campgrounds we stayed in both times is Yellowstone Valley Inn there website is as follows:
www.yellowstonevalleyinn.com it is about 30 to 40 minutes east of yellowstone. It is on the road that connects Cody WY and Yellowstone. Nice people and not very busy either. We went both times on the week you are going. The road leading to Yellowstone there are moose and bear. You can usually spot them on your way in early AM or early evening when you come back out to campground. You are only 20 minutes from Cody too. So you can go and watch the rodeo or just go and walk the wood board walk in town. We have been to south dakota 3 times too but I can't remember the name of that campground. There are many nice ones around the area. Especially around Keystone SD and Custer SD. Go on the South Dakota web site and have them send you a brochure it really helped us out. We also went to Glacier National Park last year. It was during the fires we didn't see much. Are you going thru North Dakota and all the way across Montana? If you are you will definitely find out why Montana is called Big Sky country. I will look up the campgrounds in South Dakota and post again with that info. I hope I helped you.
mamabear