Coconino National Forest
The Red Rocks of Sedona are in Coconino National Forest
The 1,856,038 acres of Coconino National Forest are divided (sort of) into 4 distinct districts: Peaks, Mogollon Rim, Mormon Lake and Red Rocks.
The Peaks District is that area mostly north of Flagstaff: the Volcanic Highlands-Kachina Peaks area. The San Francisco Volcanic Field and the highest point in Arizona are here.
The Mormon Lake District spans from the southern reaches of the Peaks District south to where Upper and Lower Mary Lakes meet, still on the Mogollon Plateau and north of the Rim. Mormon Lake is the largest natural lake in Arizona and this area is where most of the wild elk in the state hang out.
The Mogollon Rim District is that area where the Colorado Plateau drops up to 2,000' down into the Desert Canyon Country of central Arizona. This is an area of rugged countryside and huge views, where the vegetation makes the change from evergreen forests to cactus and ocotillo.
The Red Rock District is the southwestern part of Coconino National Forest, that area in central Arizona below the Mogollon Rim around Sedona and Oak Creek. This area is classed as a "high impact recreational area" and the Forest Service has instituted a "pass" program for users of this area. It is permissible for folks to stop and stretch or take a couple of photos, but if you stop in any one place for more than 15 minutes save yourself the problem: pay the $5 fee for the daily pass (longer term passes are available, too).
Coconino National Forest contains some of the most varied and sought-after countryside in Arizona: from the highest point to some of the lowest points. The vegetation varies from high alpine tundra through aspen and spruce to Ponderosa to pinon and cedar to sagebrush and creosote bush to cactus and ocotillo. From the Arizona Snowbowl to Sedona's Red Rock Country, there's a bit of almost everything here.
Scattered through the Forest you'll also come across a number of archaeological sites: some protected as National Monuments, State Parks, etc., some not. Federal and State laws are in place to try to preserve and prevent the disturbance of these historical and cultural sites, hopefully saving them for future generations to enjoy. You'll also come across old homesteads, stage stops, mine sites, railroad beds, logging camps, cow camps and other remains from more modern visitors to this countryside. For that matter, there's even an old road (now part of the trail system) that leads to the top of the Kachina Peaks (folks used to be able to drive their Model T's up there).
Oak Creek itself
In Fay Canyon, Red Rocks-Secret Mountain Wilderness
Photos are courtesy of TheArmchairExplorer, CCA-by-SA 4.0 License
District map of Coconino National Forest is courtesy of the US Forest Service