The only hiking I have done in Courthouse Wash is inside Arches National Park. I was dropped off on the park road where it crosses over Courthouse Wash, about 5 kilometers into the park. I hiked back down the wash to Highway 191, an easy walk of maybe 8 kilometers. It was May when I did this hike and there was water in the wash the entire way. Plan for this- wear river sandals, or go barefoot even. Keep on the lookout for "quicksand"- there was plenty of it on my walk.
For this hike I carried a 1:50,000 waterproof map of Arches National Park. The 1:24,000 mapsheets for this hike would be Moab and The Windows Section. You can use the Moab 1:100,000 map for planning purposes.
There is an apparently good hike in the upper section of the wash. You would enter right near the turnoff on Highway 191 for Canyonlands National Park. For more information on this hike see Kelsey's
Canyon Hiking Guide to the Colorado Plateau (see our
Guidebooks page regarding this book).
Courthouse Wash just past some large potholes, looking upstream.