I'd pick either the southern Utah Parks: Canyonlands, Arches, Capital Reef, Bryce Canyon and Zion. Or Yellowstone, Tetons and things you can see along the way there and back. Depends on where you start from in CA. You can easily spend a week or 10 days in Yellowstone/Tetons and still only see part of it.
Canyonlands needs a four wheel drive vehicle to really see it, there are viewpoints that are passenger car accessible. But there is a lot to see in the other parks. Bryce and Zion have good hiking. Bryce especially in July since it's at 9000 feet and cool.
We've been to Death Valley in July several times. Drive thrus on the way to Yosemite both times. All you can safely do is stop at various pull outs and look around for 10 minutes or so. Then get back in the a/c. A lot of roads are blocked by the Rangers during summer to prevent people from going out on them and dying. Save that for winter since you are right in the state.
