Vic,
As to hikes in the region, i mentioned Buckskin Gulch. A friend of mine prefers the Narrows as it gets you into the nice parts of the Paria faster.
I prefer mountains. You might try the La Sal Mountains outside of Moab. I think they are under appreciated, which is fine by me. My son and i were there in early June and hiked Burro Pass trail which was nice. There are a host of other trails there which are nice.
We also spend time in the San Juans of western Colorado. The Silverton area is getting crowded but some trails are pretty empty. Two of my favorite hikes are Island Lake and Columbine. Island Lake is off the Ice Lakes trail. Everyone seems to hike Ice Lakes. Every time i have hiked to Island Lake, we encountered no one after the trail split. Island Lake is incredibly aquamarine. Columbine Lake is a butt kicker at the start as most of the climb is in the first third. Nice lake. You can hike up and over to Telluride. There is also Crater Lake which is longer but flatter. In the Silverton-Ouray area there are a ton of good hikes besides these.
Farther north by Ridgeway, Co, you can head back to Yankee Boy Basin. I haven’t done it yet but a photographer friend heads up there frequently.
If you are into backpacking, there is the Weminuche Wilderness. There is a nice, long loop loop from near Vallecito Lake past Emerald Lake, up to Half Moon Lake (great camping spot), over to Flint Lake, then down the next valley. Long (43 miles). There ae lots of nice day hikes in the Weminuche.
Off the North Rim of the Grand Canyon, the Bill Hall trail gets you down to Thunder River which is impressive but crowded with day hikers from the river running trips. If you take the trail over to Deer Valley/Creek instead there is a smaller spring surging out of the canyon wall from high up and has a waterfall down stream.
South of Flagstaff, where i live, you have all the Sedona hikes. It has gotten too crowded for me there. To the east of Sedona, there is West Clear Creek which is nicer the farther up you go. Nice swimming holes, lots of jumping trout, etc. You can either enter from the Bull Pen which is easy to get to or Trail #17 from above. The later was my preferred route, but the one mile road was nasty. Fortunately, i was driving a 91 Isuzu Trooper as the skid pads were sorely tested a lot. I haven’t been there in twenty years. You can also hike in from Happy Jack.
To the southwest of Sedona is Sycamore Canyon. In winter, you hike in from the Verde River near Clarkdale. In summer from the rim (head down Woody Mountain Road (FSR 231) out of Flagstaff and you’ll need a forest service map. There are other hikes accessible from that road network.
Lots of possibilities for dispersed camping around Flagstaff as long as it isn’t the rez.
Hope this helps. Let me know if you need more.