Badlands > Needles Highway > Devil's Tower > Yellowstone > Glacier
You should cut across northern Nebraska after Omaha—I'd head to Sioux City, then Yankton, then over to Highway 20, then hit Chadron, Nebraska, before you head up to Hot Springs, SD, and the Needles Highway. Really beautiful, wildly-sparse butte country—a very different topography than the prairies of farther-south Nebraska—followed by some beautiful grasslands as you head north into the Black Hills (and it is worth it to head over to Oglala National Grassland before you turn north). You can get some famous Sioux City loosemeat sandwiches, either at the Tastee Inn & Out (if you're in a rush) or the Miles Inn (if you want a cold beer in a golblet along with it). Then there's a nice, neon-inflected historic downtown scene in Yankton—plus it was the territorial capital for a while, so there's a lot of pioneer history down that road. Then, if you've crossed Nebraska and want to stay in Chardon, there's an awesome historic hotel called the Olde Main Street Inn; it's attached to the 77 Longbranch Saloon, which has a surprisingly good local beer selection to knock the road dust off.
From Devil's Tower, I'd skip West Dakota entirely (unless you want to pop up to Alzada, MT, to have a drink at the otherwise-isolated Stoneville Saloon, a famous stop for the Sturgis-bound hordes, but otherwise a sleepy, grungy bar in a sleepy, desolate town of 23 people), and just cut straight over to Cody, WY; then enter Yellowstone from the NE entrance. Not sure how long you'll stay in Yellowstone, or how much of it you'll traverse, but I like the northern exit perhaps the best, and it provides you the opportunity to shoot up to Livingston, MT, which is another cute little historic town with some good restaurants and bars (including a solid little tiki & sushi place called Neptune's).
At that point, you'll be in Actual Montana (as opposed to West Dakota), and the sky's the limit (Big Sky pun intended). What's your route between Yellowstone and Glacier? That's a lot of country, and a lot of possible routes.