We have no first hand knowledge, however, our scenic drive book lists one for North Dakota and two for Minnesota.
North Dakota starts at Fort Abraham Lincoln State Park near Mandan, heads up and around on 1804 hitting lots of stops including the Audubon Wildlife Refuge, Knife River Indian Villages, Garrison Dam (last two on by looping west on 200A then 200 then back onto 1804) up to Lewis and Clark State Park, a side spur to Fort Buford then down 85 through Theodore Roosevelt State Park North Unit, Little Missouri National Grassland, Theodore Roosevelt South Unit with nearby Medora on 94 west that Tom mentions. It then rolls back east on 94 to the starting point. I can't list everything but it says "Not to be missed": Medora Musical, a Western-style review (Jun-Sep) in Medora; Mandan Rodeo Days in July in Mandan; Lewis and Clark weekend (Aug) at Cross Ranch State Park; United Tribes Powwow (Sep) Bismarck. Full loop is about 400 miles.
Minnesota has a loop drive listed that is pretty far north. It starts in Grand Rapids, up 38 to Effie, west on Rte 6 then Rte 1 to Northome then south on 46 and then Rte 2 back to Grand Rapids, It takes you through Chippewa National Forest with numerous lakes and rivers and refers to it as the "watery, wooded reaches of northern Minnesota". Length of the loop is about 140 miles. Features good fishing, some old growth pines over 12 stories tall, hundreds of lakes. Just realized the book has you driving the opposite direction, don't know if it matters.
Minnesota also has a lake drive listed on Rte 61 running along Lake Superior from Duluth to Grand Portage passing through numerous state parks and small towns. A portion of the northern section is in Superior National Forest. Nearby Boundary Waters Canoe Area lies along the Canadian Border. There is a 3 hour boat trip to Isle Royale leaving regularly from Grand Portage. This drive is about 150 miles one way. The book notes that Rte 61 is the state's busiest highway so leave plenty of time for the trip. .. and don't drink from the waterfalls. A quick scan of the listings shows notes on spectacular overlooks and vistas, waterfalls, hidden harbors, etc.