Coast to Coast east to west

On a trip we took from the east coast to the west coast we found ourselves staring directly into the sun especially towards the evening as the sun set. Was not a problem when we were heading east maybe because we left our campsite in the late mornings.

Easiest would be I90. With plenty of opportunity for sightseeing along the way. It’s an easy drive once your west of IL (WI/IL border).

If you are just trying to get there, plug it into google maps and pick a freeway route.

If you want to see things along the way and assuming you are familiar with and have visited the states around NC...I would suggest put in a longer day to get out to around the Mississippi. Then a second longer day to get to Denver.

There are lots of options with such a big area but what I might do (favoring National Parks):

From that point you can wander thru Colorado (Rocky Mountain NP), Utah (Arches, Salt Lake City, Dinosaur NM) up to Grand Teton/Yellowstone with a side trip to Glacier N.P. If Canada is open, swing north to Banff/Jasper NP.

Alternatively, from Arches, you could swing south and hit, Bryce Canyon, Zion, Grand Canyon, then up thru Death Valley, Sequoia, Yosemite, and up the west coast.

Are you looking at a sight seeing tour or a direct drive to your destination?
Will waiting a few days for snow to clear in a high elevation be a problem? Many of your northern passes can still get snow in June.