While visiting in March 2020, we could not find any open campgrounds in Moab or Arches. We ended up driving 10 minutes north of Arches NP and came upon willow springs. Was very crowded but still plenty of space. Easy road to drive on. Spectacular views and night skies. No amenities. 

Quick drive back to Arches NP for some amazing early morning hikes! Also near Lions Park, which has bathrooms, water, walking trails overlooking the colorado river, and grass for the pups to play.