How long do you have for the trip?
There is so much to see and do between those two locations. I would be tempted to take Hwy 128 into Moab for a few days. I'd cut across Utah on I-70 because it's a beautiful drive. Hwy 50 across Nevada has a lot of interesting places to see. OR you might drop down from Ely, Nevada to Tonopah and then take Hwy 120 over Tioga Pass (check first to make sure it's still open...it can close in October) and come though Yosemite.
I'd take I-80 home and drop down to see Lake Tahoe and you will drive right by the Great Salt Lake.
If we knew how long you had for the trip, it would help.
Utahtea