We did an August western trip last year (2011) that took us through Flagstaff, the North Rim, Bryce, Capital Reef, Arches, Moab, the Colorado Natl Monument and Breckenridge. We avoided the crowds by camping outside the Natl Parks in the Natl Forest campgrounds and doing daytrips with our toad.
The best areas were along Scenic Byway 12 in Utah. You could spend a month meandering along that route. We towed an "82 FJ40 Landcruiser up and down 10 degree grades on the two lane highway without a problem.
Natl Forests mean no water, no electric and first come, first serve so plan accordingly. Move early and avoid moving on weekends and you'll find that most camprounds don't fill up until after 5 pm.
Our campsite along the Colorado outside Moab was the only real hot spot of the trip.