If you need a campground in Bismarck or Mandan and if you can get into General Sibley Park my son said it was really nice, but was filled up when they were there. http://www.bisparks.org/Facilities/sibley.asp
They stayed at a small place in Mandan. Colonial Motel & Campgrounds 4631 Memorial Hwy, Mandan - (701) 663-9824 We had passed by it in 2007. It is in an commerical area, not very resort like from the entrance off Memorial Hwy, however later on we rode by the back side on a bike path and it looked good. As it turned out it had water, electric and sewer hookup for $19. The bike path leads accross the river and by the zoo and a nice park.
From the web site Gen. Sibley is $20 with water and electric but the setting is much better. Closer to the river. Both have trees. At Colonial the sites are very close together. Sibley they are space out. Sibley has over 100, Colonial maybe 20. It did not fill up while my son was there.
Fort Lincoln State Park also has a nice campground & neat things to see (It was where Gen. Custer was living before he went on his last ride) and is by a river:
4480 Fort Lincoln Rd
Mandan, ND 58554
In July of 2007, we stayed at the KOA Bismarck, over priced and dusty. We had passed the Colonial campground but it did not look very inviting from the entrance, but seemed OK from the back. Not a bad price with water, electric and sewer for $19.
Sofia you wrote, "We are stopping in South Dakota to see family and then heading out on I-94." With I-94 being in North Dakota, I assume your stopping in SD means the stop is near the ND/SD border. I second Kevin's recommendation of Medora ND to see T Roosevelt National Park(south unit) The campground is very nice indeed. We were there in June. It is near the ND boarder with eastern Montana.