Most anytime from the end of June to end of August is good. Later June to early July is my favorite. 21 June is the longest day and up here our twilight lasts for 45 minutes to an hour after sunset, father north you go the later it sets. GREAT summer evenings. It is the tourist/ travel season but most people leave ND instead of come here. No crowds or traffic hold ups, unless you get some road construction.The roads are good, mostly flat. Gas stations are all over the place. Just remember in ND everything is spread out. 360 miles east to west on I-94 and hardly a curve in the road.
If you prefer to state or federal campgrounds this route would my choice would be.
Sorry this is going to be so long, but ND is a large place and everything is spread out.
Enter the state by I-29, go to Fort Ramson State Park real nice campground on the Sheyenne River. Spend a day exploring that area.
Next head up to Devils Lake and stay at Grahams State Park. Mostly fishermen stay there but a nice place, kind of like an island in Devils Lake. Take a day or two in that area. Go to Sullys Hill Game Reserve. Right next to that is Fort Totten Historical Site, worth the stop. Couple of nice little museums in town. If you like to fish Devils Lake is one of the nations top walleye, perch and northern producers. Several guides work on the lake.
After there head north to the International Peace Garden Peace Park. A joint effort park between Canada and the US. They have a campground there but I have not used it.
From there go to Riverdale/ Pick City. They are on the east and west side of the Garrison Dam. Dam tour is worth the stop.
From there you back track about 10 miles to Hy 83 and go to Washburn to the Lewis and Clark Visitor. They spent the winter in the area (179 days I think). Make sure you take in Fort Mandan, a rebuilt fort like what Lewis and Clark stayed in. Amazing history tour there.
When finished there go south to Bismarck and stay at Fort Lincoln State Park. Fort Lincoln is where General Custer headquarters was before he left for Little Big Horn. The fort has rebuilt Custer's house and some other buildings. They have rebuilt an Mandan Indian Village that is very interesting. Bismarck has a lot of things to offer. A river boat cruise, you can go up to the top of the state capital building. 18 stories high and the tallest building in ND. By the capital is the stat heritage museum a must see.
The trip from the peace gardens to Fort Lincoln should only take a day.
When done in Bismarck head west to exit 110, Glen Ullin, take HY 49 south to Elgin, get on HY 21 go west to Regent. From Regent go north on the Enchanted Highway. A local man has made some steel sculptors that are really nice, worth the side trip. When you get to I-94 north of Regent go west to Medora, only 60 miles. Pend a couple of days in Medora, go for a drive thru the park, take in the pitchfork fondue and see the musical. Take a day trip to the north unit of the park. 70 miles one way but worth it.
Leaving Medora you are only 275 miles from Custer SD, which is on the south side of the Black Hills. Deadwood is only 210 miles from Medora.
If you have any questions just ask. I have lived here for all but 1 1/2 years of my 62 and am one of the few who like it here.
Enjoy your trip here.