Hike the Thompson trail in Eastern Arizona.
From the signed trailhead, walk downstream along the West Fork of the Black River. There are actually two trails here. The hiking trail stays close to the river and can sometimes be tricky to find. If you loose the trail your best bet is to search near the river to pick it up again. Depending on the flow of the river and recent rains, it may be a bit marshy in spots during this hike. The other trail is for mountain bikes and horses and follows an old dirt road.
The walk along the river is very enjoyable, as this year round river accompanies you for the entire hike length. During the hike you will pass a few man made waterfalls along the river. The purpose of these falls are to protect the native Apache Trout in the river. In this section, fishing is prohibited. However, you will likely see fishermen along other parts of the creek.
We hiked this trail to the point at which the West Fork trail comes in from the left and a creek comes in from the right. This makes for a good turn around point.
If you like, you can take the old dirt road back to the trailhead. It is further away from the creek, but has some unique views.