They prefer dense shrubby areas that have lots of hiding places. That's probably why I don't see them in my neighborhood, where most of the yards are sparsely landscaped with gravel and a just a few plants.
This young cottontail is posing like a statue. Does it think I can't see it because it's face is partially hidden behind the bush?
Finally, it hops away to find a better hiding place. Desert cottontails are an important food source for many animals including birds of prey, snakes and coyotes. Unfortunately, most cottontails don't make it past their first year. Bonus image: Here's a picture of my son running at Sabino Canyon. A cottontail happened to be crossing the road as the photo was snapped.