With a little extra time you could also stop at Zion NP and possibly Bryce canyon in Utah. From Moab you could head to Bryce canyon via Capitol Reef to Torrey and then take Utah Scenic Byway 12. Another option from I70 would be to head west from Cedar City to the ET highway [NV375] to US6 through Tonopah. You can then link up with CA120 which goes into Yosemite NP and crosses the Sierra Nevada on the spectacular Tioga Pass.

You will still have to pick and choose and each and every park is quite spectacular in it's own unique way. If I were heading to Oakland, I certainly wouldn't turn down the drive into Yosemite, it's spectacular !!