So I was discussing your plans with my husband this morning over breakfast.
If doing northern California, I would fly into Reno or San Fran. Let's say San Fran b/c you want to see a city. Drive north on the coastline...it's all beautiful and that way you can see the redwoods, which are a must-see (IMO). If you want to go all the way up to or near coastal Oregon (even MORE beautiful IMO), then my particular favorite spot is Prairie Creek Redwood State Park/Gold Bluffs Beach/Fern Canyon, just north of Eureka, CA. Easy short trails through the redwoods, spectacular but easy hike through Fern Canyon, elk herds, tremendous beach, usually not as packed with people as some of the parks.
https://www.visitredwoods.com/listing/fern-canyon-in-prairie-creek-redwoods-sp/464/If I were hitting southern OR, it's fun to shoot up to see Crater Lake and Ashland (lovely downtown, theater community, huge Shakespeare Festival, some nice vineyards in the area if you are into that). Then back south through the Cascades and the Sierra Nevada Mountains, stopping off at Lassen Volcano NP, Lake Tahoe, and Yosemite NP, and then back across to San Fran. If you want to go a little further south, you'll be close to King's Canyon/Sequoia NP and Death Valley NM, which I've never been to but am dying to see.
****
If I were doing a Southwestern/Western trip, now that DH and I discussed it, I'd probably skip New Mexico. Personally, I'd fly into Salt Lake City, Utah, and wander down to Bryce and Zion. Zion is spectacular, though very crowded, but can be enjoyed just driving through; and Cedar City is a nice town to stay, with an active theater community so you might take in a play while you are there. I have not yet seen Grand Staircase/Escalante but you can do GS/E on the way south. Contine down to the north rim of the Grand Canyon (much less crowded than the south rim). I think going as far south as Petrified Forest/Painted Desert in AZ might be pushing it, unfortunately, so I'd instead drive east through Monument Valley, then into the Four Corners area (Mesa Verde NP in Colorado is amazing, and if you want to get a feel for great mountain scenery, Durango CO to the Telluride/Silverton area is a beautiful drive). Then start looping back up, hitting Canyonlands NP on the way.
It's ALL SO GREAT. By the time DH and finished thinking of recs for you, we realized it's been 15 years since we have road tripped in either one of these regions. Guess what we'll be doing this fall? Damn, it's making me want to pack right now.