Your best bet would be to go to the website for our auto travel club called AAA (Triple A) at
http://www.aaa.com. Click on the link for "Travel" "Maps and Directions" then "Create a TripTik". Put in the places you would like to see - there are drop down menus where you can say Cities, National Parks, etc. and go from there. You will end up with a nice little map of where you would like to travel, how long it takes, best roads, other sightseeing places, etc. It might give you an idea of what you can do. I think you might need to be a member if you want to download or a hard copy of these things. We are members and can send you tons of stuff like TripTiks, AAA Tour books, etc.
I did a quick one for you and it seems like you are trying to cover a huge distance in a smalll amount of time. We are a humungous country. Not sure if you want to spend a little time looking at the Grand Canyon and then 8 hours driving to your next location kind of thing. Also, is there a reason why you want to fly into Denver? An alternate might be less worry of snow. Denver and through the mountains of the continental divide can get snow even in August (I've gone through it - not fun to drive switchbacks in snow). Alternately the desert can be pretty warm in May-June.
BTW, on the sample TripTik I had you going from Denver, Arches NP, Bryce Canyon NP, Zion NP, Grand Canyon (South Rim) NP, Sedona (I added this), Las Vegas, Death Valley NP, LA, Sequoia NP, Yosemite NP, San Francisco. 2300 miles in all (driving it straight)...and there are so many other places to see along the way like Laguna Seca, etc.!!