We bought a place in Sedona last year, and will be living there part time going forward. So far, have done just a bit of road riding there, so I can provide a bit of input on that. Haven't explored gravel yet (my road bike isn't really set up for gravel yet).
Here are a few thoughts... The "hub" of the town of Sedona is at the intersection of Hwy 179 and Hwy 89A (used to be know as "the Y", but since replaced with a roundabout). Heading south from there on Hwy 179, there's a stretch for about 9 miles (past Bell Rock and through the Village of Oak Creek) that has bike lanes. The bike lanes end to the south at the Red Rock Visitor Center. Hwy 179 continues south from there down to Interstate 17, but I haven't ridden that section (no bike lanes, and it's a 2 lane road with narrow shoulders and 50+ speed limit).
As you pass through the Village of Oak Creek, there's an interesting spur route you can take out to the back side of Red Rock Crossing. No bike lanes, but relatively light traffic and reasonable vehicle speeds. The first 4 miles (to Verde Valley School) are paved, and then gravel road for another mile or two to Red Rock Crossing trail. I felt safe riding that road, too.
Going back to the "hub" I mentioned above... The other option is to take Hwy 89A west (well, southwest, to be precise) toward Cottonwood. The first portion out on 89A has bike lanes, but also more traffic as you pass through the commercial district known as "West Sedona". I've ridden that, and it's fine (except there are a number of stop lights along the way). Once you pass the emergency medical facility, and the high school, the road opens up. It's 4 lane, divided, for most of the rest of the distance to the town of Cottonwood. Highway speeds, but a good size shoulder to ride on. I haven't ridden this section yet, but I've seen quite a few cyclists out on it. The total distance on this Hwy 89A segment from Sedona to Cottonwood is about 18-20 miles.
Along that 89A segment, there's also a loop road you could add to your ride (Red Rock Loop Rd). The north end of that loop road is at the stop light for the Sedona High School. This loop road is fairly narrow, but traffic speeds are generally pretty low. I haven't ridden this loop yet either, but again I've seen a number of cyclists out riding it.
You could also reach out to the Verde Valley Cycling Coalition [
https://www.vvcc.us/ ], a local cycling group. They organize both road and MTB rides (and I assume they do some gravel, too), so they may be a good resource. Here's a link to some road rides they like [
https://www.vvcc.us/page-18096 ]. Also, here's the bike shop I use when I'm down there [
https://absolutebikes.net/ ]. They have locations in both Sedona and Flagstaff. They are a bit more focused on MTB than road, but they may also have recommendations on good road and gravel routes.
One note if you ride up in Flagstaff. Be ready for the elevation. Sedona is at 4,500 ft, and Flagstaff at about 7,000 ft. Impacts me more on runs than on bike, but I definitely notice it when I do aerobic work up in "Flag".