I have not really gone hiking since my days in Arizona, but there is one important rule to remember, never hike alone. You don't have to out run the bear if you can out run who you are with.
@Peaches they have a ton of tarantulas, but those are really harmless, I've heard of some cougars/mountain lions, but I think if you stay on the main trails it is rare. The biggest problem is javalinas that look like wild pigs and travel in packs, they do not have tusks like boars so not completely dangerous I guess . Snakes of course are a danger, but those are everywhere.
@BridgeOvertroubledWaters Thank you. It's from Sedona, AZ, where the Colorado Plateau starts to break up, about an hour drive south of the Grand Canyon. Beautiful part of the country.