>>574497Grand Canyon on the Rim has an ass load of people, but the views you get are stunning. Lots of trails to do day hikes and I highly recommend backpacking down there. Its absolutely beautiful. Sedona has an ass load of people too, but you can get out in spots that are more secluded.
You can also check out Havasupai falls. Nice place to go backpacking, its just that It became outrageously popular and its kinda turned to trash. Lots of people there because Its an easy trek and its beautiful.
There is also Paria Canyon near Page where you can backpack, but It is considered one of the more dangerous hikes on the planet since its in tight canyons and in the raining season you can easily get killed by a flashflood. Place is nice looking though. One day Ill work up the courage to do it.
I go to school in Flag and its a nice /out/ place, and there's a shit ton of places to go hiking.