lucrativetravels.com posted a surprisingly good list:
Wet Beaver Loop
Picacho Peek
Kendrick Mountain
Paria Canyon
We name Paria Canyon the best hike in the entire S.W. USA.
The other three I’m currently researching. … Especially since I’ve just arrived in Arizona. We drove between Tuscon and Phoenix yesterday past impressive Picacho Peak.
Wet Beaver Loop
The Wet Beaver Loop is not a trail that should be hiked by a novice. The trail is a twenty-two mile loop so you should plan on taking a couple of days to complete it. …
Picacho Peak
The Picacho Peak is a hike that that will provide you with the opportunity to admire the Sonora desert. Although the trail is only a seven mile round trip, you need to be aware that much of it is extremely steep and that there are many switchbacks. …
Kendrick Mountain
If Picacho Peak is more than you feel comfortable handling, you might want to consider the Kendrick Mountain hike. This particular hike is 9.2 miles round trip. When you reach the summit you will find a cabin and have an amazing view of Mount Humphreys, Red Mountain, and Sycamore Canyon. On a clear day you will even be able to see the Grand Canyon’s north Rim. …
read more – lucrativetravels.com
besthike.com 
That’s a very poor post from “lucrativetravels”, as besides giving almost no stats on each hike, it doesn’t even say where they are located.
Having noted that, I agree Paria is one of the best hikes in the SW. However, I prefer the Buckskin-Paria Loop, as it’s possible to do that w/o paying for a shuttle.
One also notes the Grand Canyon is in the state of Arizona, so to leave that out of any “Arizona Best Hikes” list really doesn’t make any sense.
Lastly, instead of those other little peaks mentioned, Mt Wrightson is far more worthy. 11.8 mi r/t; 4,000′ vert; all single-track; rocky outcrop for a summit. It’s an hour south of Tucson; check it out now.
Thanks Buzz.
… I was wondering why lucrativetravels would be posting a list of “best hikes”.
Any hike in the Sycamore Canyon near Cottonwood and Sedona is well worthwhile. The Chiricahua National Monument in Southern Arizona has 17-miles of hiking trails spanning small canyons and a maze of hoodoos. And the Araviapa Canyon in Central Arizona is a wild, wet primitive area where you need permits for hikes.