I'd recommend Hwy 2 from Glacier to Kalispell, then US 93 heading south from there. It skirts the west side of Flathead Lake. Next to St. Ignatius is the National Bison Range, a very interesting, and very under-visited member of the National Park Service. They have the largest herd of free-roaming bison outside of Yellowstone National Park. Very worthwhile.
After you hit Missoula, (a fine place to spend the night, if you want), you can take Interstate 90 east to Butte, then I-15 south to Hwy 33 east, right before Idaho Falls. Follow Hwy 33 east through Rexburg to Jackson, and you'll be at the Grand Tetons. It's a great drive, good roads, nice scenery, and it won't wear you out. It'll be 8-9 hours of driving, give or take, no matter which route you take, but you'll arrive a lot less tired than if you're driving narrow, windy roads over unknown terrain. The scenery at Tetons will make up for anything you didn't see on the way down.
Dave