Much will depend on what your interests are.
We enjoyed one trip traveling on the old hwy 2..one of the earlier Coast to Coast highways. Loved seeing the smaller towns and a more intimate view of the USA than traveling the interstate freeways.
Have done I94 multiple times and stopped at the Teddy Roosevelt National Park. Came into Yellowstone from the Northern entrance and traveled down through the Tetons to Utah. If you travel further North there is a Lewis and Clark Interpretive Center in Twin Falls Montana and from there you can visit Glacier Park (multiple interesting lodges and the going to the sun hwy), perhaps up into Canada and visit the Prince of Wales Hotel. Or you could drop down from Missoula (might get a sandwich at Montana Great Harvest bakery), then on to Hwy 12 through Idaho to Oregon. Hwy 12 is an interesting and historic route. There was a bit of gold mining along the river and (to me) a very pretty but twisty drive. In Oregon there is Crater Lake and you could head toward the Coast and visit the Oregon Caves then down to see the Redwoods in upper California.
I90 has more to see as there is the Lewis and Clark interpretive center at Chamberin, and of course Wall Drug, the Bad lands national park, Mt Rushmore, Custer State Park, the Wind Cave National Park (black hills national forest), Yellowstone National Park from the East side.
On I80 you can stop at Iowa80 Worlds Largest Truckstop. Fun to do at least once ;-). The National parks in Utah are great. We enjoyed Bryce, Grand Staircase, Capital Reef and Zion. Did not have time to see Canyon Lands. will have to do that on another trip.
So much to see so little time.