Teddy Roosevelt National Park, has camping in designated areas, you'll have to go on the outside though, no hunting in the Park.
I've camped a lot on the State Wildlife Management areas. The larger ones often have fire pits shelters and toilets. I don't think there is overnight use on the Federal WMA's
There are a few million acres of National Grasslands In Western North Dakota. Perty Much N,S,E and West of the Teddy Roosevelt. All public land and camp where you like. The Law is "motor vehicles on established roads only". Lots of side trails you can drive on. I think you can camp 50, maybe 100 yards off a established trail on Federal Lands. "pack it in, pack it out is the Law".
There is the Buffalo Gap National Grasslands Campground just West of the River a couple miles and just off the interstate. VERY NICE! Has facilities if you don't go for the remote stuff.
The National Grasslands in ND are some very nice country. Lots of true native grasses and plants. I highly recommend a visit. Good hunting too.:thumbsup: