We did this trip about 20 years ago but it was one of the most amazing holidays we've been on. The scenery was just spectacular and a photographers dream. We did it the other way round to what you are proposing and took 2 weeks.
Phoenix - literally stayed the night and left first thing in the morning
Grand Canyon - just amazing. I could have spent days there just staring at it. It is something else and the colours change depending on the angle of the sun.
Monument Valley - a last minute decision to do this as it was out of our way but so glad we did. It was incredible. Such an amazing landscapes. They used to do jeep safaris round it and it's well worth the money they charge, you get to see bits you can't get to on your own.
Zion Canyon - pretty impressive great colours again.
Bryce Canyon - spectacular scenery again. We preferred it to Zion. A word of warning it's very high over 10,000 feet mostly and you notice the thin air.
Lake Meade and Hoover Damn - ok it's on the way to Vegas. Some nice views.
Las Vegas - Vegas is Vegas we just stayed a night and a day.
Death valley - a little disappointing. Not very interesting in my view and not that hot when we were there in late September.
Sequoia National Park - amazing place. You cannot believe how big trees can get.
Mono lake - an interesting place worth a visit.
Yosemite - spectacular again but, as the poster above says it was pretty dry in September so no waterfalls.
San Fransisco - we liked it Thought it was a nice city. Got some sights - Golden Gate bridge, Alcatraz, steep streets, street cars.
That's it. If you want any more info I will try my best to remember.