CA to VA
So a cousin of mine is moving to Virginia from California and has offered to fly me out to California (and enjoy the warm weather for a few days) if I would be willing to accompany him on this long trip from Irvine, CA to Arlington, VA. I believe he would like to complete the trip in 4-5 days so most of our stops will be to rest. Not sure what vehicle he's driving back but suffice it to say it will just be the 2 of us.
I'm posting here to get some ideas of places that could ABSOLUTELY be worth seeing on a time budget. Like if this could be my first and last time going cross country (almost literally coast-to-coast) - what is worth most seeing in a conceivable route (we'll likely be taking the most time-efficient path across country if that helps).
Welcome to the RTA Forum!
What's "worth" seeing is nearly impossible to say, because there are millions of possibilities and we know nothing about what you find interesting. However, RTA's map center is decided for exactly the question you've asked - as it can provide dozens of potential stop ideas right along your route.
You do need to note that 5 days is really the minimum needed to do this trip safely, and even that will require being on the road for 10+ hours a day, and that assumes good weather the whole way. That may leave time for a couple of short stops for rest at places right along the highway, but significant detours - including driving say 2-3 hours out of the way to visit the Grand Canyon - really would be too much. 4 days would require driving too many hours per day, even with 2 drivers, to be considered safe.
My husband and I went from San Diego CA to western VA in 5 driving days.Here is a link to that trip. Our first day was 375 miles from San Diego to the Phoenix area, second 600+ miles to Santa Rosa, NM, third 600 miles to eastern Oklahoma, fourth to central Tennessee at 600+ miles, and then we made 600+ miles to Virginia. We mostly took I-40 to I-81. Had we not stopped in Phoenix, we might have gone to Holbrook, Amarillo, Little Rock, Knoxville, and Staunton for our overnights.
Five days is your minimum...and that's with 600 mile days. If you are driving in the winter months, you may need to allot another day. BTW, we did NO sightseeing along the way except for what we could see out the car windows, and our trip was in July.
Yes, If Things Go Right
While it's true that you will need all five days to complete this trip safely, and that only if you take the most direct route (basically I-15/I-40/I-81/I-66). There are two of you to share the driving load. Note that doesn't mean that one of you gets to sleep. It means that one of you will be able to act as navigator/radio operator/attendant/safety officer while the other takes care of piloting.
In any event, you will need to keep your 'stops' relatively close to the main highway, with one exception. If you haven't seen it, by all means take the few hours it will take to 'detour to the Grand Canyon by using AZ-64/US-89 from Williams AZ through the park and back to I-40 at Flagstaff. Other quick stops could be at the Petrified Forest National Park, Petroglyph National Monument in Albuquerque, Cadillac Ranch outside Amarillo, the Oklahoma City Memorial, Mud Island in Memphis, and Smoky Mountains National Park. Note that you will not be able to make all those stops, but any combination will make for a great trip. You'll have to figure out as you progress on your journey which ones you'll have time for. I would recommend that work out schedule.
Grand Canyon, Eastern NPs
I can heartily recommend the half-day drive-through loop through the Grand Canyon, exactly as suggested (which is essentially the only route available).
Back this way, be aware of the high elevations and early and severe winter weather in the Smokies. Much of the Blue Ridge Parkway (BRP), particularly the higher elevation segments down that way, are closed much of the winter. Just this week I read of a scheduled closure of a segment near Asheville where bridge repairs will require longer-term closure.
As you head from Knoxville up I-81 towards DC, you can test short segments of the BRP between Roanoke, VA and its northern end at Rockfish Gap and/or all or parts of the Skyline Drive (SD) within Shenandoah National Park. In each case, lower elevations than those here in NC generally mean fewer and shorter winter closures.