If you had a shload more time, I'd consider a loop like this:
1. White Sands National Monument (Up I-10 to Las Cruces, then east on 70)
2. Grand Canyon (West on I-10 to Phoenix, then I-17 to Flagstaff, then HWY 180?)
3. Antelope Canyon Photo Tour (HWY 89 to HWY 98)
4. Lake Powell (HWY 89)
5. Zion National Park (HWY 89 to HWY 9)
6. Bryce Canyon (Back across HWY 9 to HWY 89, then HWY 63)
7. Salt Lake City and Temple Square (Go West to I-15, then head North)
8. Park City (East on I-80)
9. Columbia River Gorge (I-80 West to I-15 North, then I-84 West*)
10. Portland (You made it!)
11. Oregon Coast (Perhaps HWY 99/18 to Lincoln City, then down HWY 101)
12. Redwood National and State Parks, Fern Canyon, etc.
13. Agate Beach at Patricks Point State Park? Lots of seals at Patricks Point...
14. San Francisco
15. Yosemite (Whatever route Google says is best
16. Death Valley
17. Las Vegas
16. Back to El Paso...
According to Google, hitting everything on this list would require about 70 hours of driving. Yikes. That would be 7 hours every day, without stops, so that definitely qualifies as a whirlwind tour (although only 2 hours a day more than Google's recommended direct routes). Better to have 30 days for this one...
* If you can hit Dead Man's Pass at sunrise or sunset, all the better! Not many other photo ops between Salt Lake City and the Gorge.