What month are you doing this trip? More hospitable weather goes from November - Early Spring. Yellowstone in November would be an ADVENTURE though!
I think Chaco requires half a day. It depends though would you also visit Aztec National Monument on the way from Durango? I think Aztec would take about an hour. I wanted to stop here as we were driving by, but some of the passengers lacked my interest in another Native American site!
Mesa Verde depends on how much of the park you want to see, there are 2 distinct areas. If you choose to take both routes it will be a whole day. If you choose 1 area it will take half a day. Cliff Palace is the most common route (more crowd but the most impressive cliff dwelling)
Some of the Arizona sites I will provide a couple extra details. In case you find yourself that way.
Petrified Forest National Park (can be visited comfortably in 3 hrs (Highly recommended, beautiful landscape)
Flagstaff, AZ Lowell observatory at night (was on the previous US tentative list) Hard to beat the star visibility around Flagstaff.
Walnut Canyon National Monument (worth a short stop 1 hr, but since you will already see many amazing Native American sites, probably not worth the time)
Sunset Crater Volcanic National Monument & Wuptaki National Monument (sites are right next to each other, together they can be visited in about 3 hrs. Wuptaki is as impressive as many sites in Chaco and Sunset Crater is otherworldly in its landscape)
Concerning Vermillion Cliffs I have never visited the site, but check out the pics here.
When I first saw the picture below I immedietly wanted to visit the national monument. However, a special permit is required to visit this area, and I don't know how long the hike would take. This area would be a place you would pass on your way back from to SLC.
http://loscuatroojos.com/wp-content/uploads/2007/07/coyote-buttes-The-wave.jpghttp://www.blm.gov/az/st/en/prog/blm_special_areas/natmon/vermilion/photos.html