If I'd never done it, I'd hike: 2 days rim-to-rim in GC, a day in Zion, a day
In Bryce, a day in Capitol Reef.
If I'd seen all of those, I'd take a couple days driving up 1 to Avila/Pismo Beach (inc stops in San Luis Obispo and at Hearst Castle) then Monterrey, then across CA to Yosemite for a couple days, then a day at Tahoe before driving across the forsaken wasteland that is Nevada.