I did a bunch of this only in reverse order. Are you purely landscape or is wildlife a possibility as well? If so then go west out of Denver and make a side trip to either Mount Evans or Rocky Mountain National park. You stand a decent chance of seeing moose in Rocky Mountain NP, mountain goats in Mount Evans. Mount Evans is less out of the way. Then head on towards Grand Junction. It's not too out of your way at all to drive through Colorado National Monument, though when i went through in the middle of the day it seemed pretty meh to me.
Go to Moab. At Moab go see the Fischer towers at sunset one day. Go to Dead Horse Pt, spend a day or two seeing Arches.
Drive south down to Kayenta. You'll drive through Mexican Hat, another photo op. It's also not much of a detour to see the Goosenecks of the San Juan.
I skipped Monument Valley. You pretty much have to have a guide to get to all the really well know spectacular locations.
Drive over to Page, AZ. Get up early and shoot Horseshoe Bend. Then drive out to the place to enter the drawing for "The Wave." It's about 20 miles west of Page, I can't remember if it's in Utah or not, but double check because Arizona doesn't do daylight savings time and you can get messed up on your times when you cross from one state to the next. They draw 10 names a day that let you hike out the following day to Coyote Buttes "The wave." If you win the lottery, write off a day in Vegas. If not, you just lost a little time. Then go back to Page and to lower Antelope Canyon. Mid day go to upper Antelope to get the sunbeams coming through. Don't go with one of the tours in town, just go across the road from lower Antelope pay your money and have them take you out. Then you can spend all the time you want and come back when you want. Tripod a must, angle finder nice so you don't have to bend so low, you'll be shooting up a lot, 20 second exposures not uncommon.
I think you can get out of Page in time to get over to the north rim of the grand canyon by sunset. Book a room for this NOW. If you won "The Wave" lottery no problem you can still drive back to it from the North Rim the next morning. There is no hotels close to the north rim other than the one right at the north rim, so if you don't get that one you'll have a long drive out.
Ok so new day, North rim at sunrise, you'll either be heading to "The Wave" and then to Bryce Canyon or straight to Bryce. It's not too far a detour out of Kanab to the Coral Pink sand dunes. Not the best in mid-day but still worth seeing with your eyes. I stayed in Panguitch once, and camped in Bryce once. Panguitch isn't too far away. Hit Bryce at Sunset and Sunrise the next day. Maybe spend two days here. Do a hike down into it,(will be brutal hot though).
After Bryce drive over to Zion. There's some good stuff outside the actual canyon, on the road to it from the east like you'll be going. You will have to shoot late in the day, and early there, not just because of the lighting but because it's just roasting hot there in the summer. Also you no longer can just drive into the actual Canyon, you have to take a shuttle bus. You can also bicycle, there's probably bicycle rental in Springdale, don't know for sure, we had our own bikes. We could park close to the entrance and bicycle in, it's a fairly easy ride. Book ahead in Springdale, the hotels there sell out early. So do the camp sites.
The big thing I want to do in Zion is hike deep up the stream to the racetrack. Unfortunately it was early June when I was there and the snowmelt was causing the stream to flood huge. BTW it was super hot even in June. In July maybe the stream will be down low enough that the only worry will be a flash flood. If you're not hiking to the race track i'd say spend maybe 2 days there just to get 2 sunsets then head out.
Now you can go to Vegas or take everyones advice and skip it. Vegas in the summer is just hell, HELL I TELL YA. It will be 95 degrees at night there, forget about movement in the daytime.
So drive out of Vegas, and check out the hoover dam, they're building that stupid bridge away from it now, so drive across it while you can. Then head on over to the south rim of the Grand Canyon. Again book ahead. Stay at a couple of the better lodges if you can, otherwise stay at a hotel south a few miles out of the park. The lesser lodges have horrible ratings on tripadvisor.com. You can see it all in a day, take photos maybe one sunset, a sunrise, and another sunset then head east, not many hotels out this way though. If it was me i'd drive back to Denver through southwest, Colorado. Then you could go to Mesa Verde NP in the very southwest corner. You might also consider seeing the Grand Canyon south rim, then driving south back to the interstate and heading east. You can then see the Painted Desert/Petrified Forest, and then turn North and see Canyon De Chelly, on your way back towards Colorado. Zig and zag your way up through Colorado, maybe see Pikes Peak.
I've probably included too much stuff. If it was up to me i'd skip Vegas, and try to add in Canyon De Chelly and Mesa Verde. I did this trip plus i'd already been to Yosemite and Death Valley when I got to Vegas. We drove on through, and I like Vegas. It was just really out of place compared to all the natural wonders. Vegas is the height of American culture, so plastic, so fake, and disposable. Something gets old, you tear it down and build a new one. The scenic locations around Vegas don't hold a candle to the others on your trip.
Have another day? you could take a boat tour on Lake Powell out of Page to Rainbow Arch. Or just do nothing. You're going to be go go go driving all day, taking pictures until late, eating dinner, then sleep, up early, more pictures, drive all day. You're going to be worn out. Build in a vacation from the vacation if you can.
You should seriously consider buying these
http://www.martres.com/m_books.htmlHe has maps, locations, times of day, times of year etc. all layed out for you. You just need to pick the ones you want and go from there.
A few final reminders. It's going to be SUPER HOT. Hiking will be pretty much not worth it during the day. 2. The distances aren't just 300 miles, it's 300 miles of boredom. You'll see some great stuff, then see nothing but dead grass for hundreds of miles. I hope there's at least 2 of you that can drive. 3. Weather. You'll get some afternoon thunderstorms, and you only have one day at a spot so you might not get anything. When I went to the wave it had stormed over at Bryce, and the flash flooded down to the wave. I wound up with a 10 mile hike instead of 4 or 5 because the road was washed out. This isn't the norm, but storms can throw you off schedule in a variety of ways.