Yosemite seems a bit far for that length, 24 hours of driving, especially when all the mountain passes are closed. Tioga Rd and Glacier Point Rd will still be closed, so you're limited to the Valley (which is awesome to see, but crowded), Hetch Hetchy and Wawona area, which just had some bad fires. So you'd miss out on some of the best parts. You could also hit up Sequoia and Kings Canyon, but with that amount of driving, you'd probably have 5 days to enjoy out there.
Southern Utah would give you more time (obviously its closer). There's a Utah National Parks thread that has good stuff in it, but a week is possible to go to a lot of great places.
Davis Mountains (Indian Lodge for hotel) or White Sands or Carlsbad would make a decent, place to stop on your way out.
The area around Page, AZ is awesome. You can get your token Instagram pictures at Antelope Canyon and Horseshoe Bend