There are a couple of ways you can go. If you go through the back gate and over the drive is about 5-6 hours. You could go to Merced and drop down to Sacaramento and into Reno and I think the drive would be close to the same time frame give or take a hour or so. I think I would be inclined to go through Mariposa and over.
About 150 road miles.
Reno is about 200 miles away from Yosemite Valley. You would have to take Tioga Road to the north of the valley.
The one in Washington is 961 miles from Yosemite.
It is 275 miles via CA-88 and CA-49.
650 miles
141 miles
765 miles
about 200 miles
834 miles
Reno's area is 69.3 square miles.
281 miles
400 miles