[twindman]

I would heartily disagree with suny. From Nashville to Billings is 1600 miles. Unless you don't stop and average 50 mph, you would have to drive 16 hours a day. By my calcs, you need to average 370 miles a day of driving. So just look at the map and figure where 400 miles +- takes you. I used to drive 350-425, but I have slowed down and aim for 250-350. Get in early and have time to rest up a bit and cook supper.


As for part 2, since you will be west of Yellowstone I would look around West Yellowstone for campgrounds. The best is Grizzly RV PArk but very expensive - about $100 a day. Others in town are cheaper, but small tight sites per the reviews. If you go North or West there are some campgrounds that are less and roomier, but I didn't want an extra 20-30 minutes of driving to the Park gate. Also the Park is VERY busy. Go early (tho I prefer sleeping in a bit) and expect most parking lots to be full by mid day or so. If you have never been, take many days to see wolves (if lucky), grizzlies or other bears, MANY buffalo and elk and again if luck, a moose.
Utah is going to be VERY hot in late summer. I think there are about 6 National parks/monuments spread out over the state. Definitely see Bryce and Zion. We spent a week or so and by the end I was actually tired of red rock!! Beautiful, but after a while......
If you see Zion/Bryce you will be in Southern Utah, and Estes park is in the northern 1/3 of Colorado. So back tracking is required. Estes park isn't much, but I assume you want to see Rocky Mtn National Park there.
As you can tell, I have seen the area often as I live in AZ. The WEST is VERY BIG - LOL. Have fun.
p.s. I use campgroundreviews.com to pick a campground. Good to see other's reviews and ratings.