Salt River - White Mountain Apache Tribal Reservation, Arizona

Salt River Canyon in the White Mountain Apache Tribal Reservation is a breathtakingly beautiful valley in an otherwise starkly dry and hostile rugged mountain desert. Summer can be extremely hot, fall is comfortable.
From Globe follow the AZ-77 / US-60 north-east for 38.2 miles. After crossing a bridge over the Salt river, immediately make a left turn, there usually are tribal reservation information signs. You can park here to start hiking or follow the usually well-maintained gravel road about 4.25 miles to where Cibecue Creek flows across the road. The parking area is before the creek, which can be impossible to cross in a regular car.
You can go rafting on the river, continue to hike or mountain bike further along Salt River on the gravel road/trail on the other side of the creek, or go canyoneering in the Cibecue Creek, see komoot.com/highlight/151959 (Danger: Flash Floods, do not enter if it might have rained in the mountains).
A White Mountain Apache Tribal permit is needed to hike or do other recreation here (rafting seems popular). There is a self-registration booth at the turnoff from Hwy 60, but no self-registration envelopes nor staff were available to sell one in November 2013, so better buy permits online before reaching this out-of-phone-signal area:
wmatoutdoor.org/purchase_permit.html - It asks to create a username/password. Click on Special Use Permit, Black River/Salt River, $15.00 as of 2013.
Update 2020: $30 per person for the Cibecue Falls; $9 for vehicle recreation.