North of Moab in Arches National Park, there are several offroad routes open to mountain bikes including Devils Garden Loop. These mountain bike routes are best a day or two following a rain cycle since they can get pretty sandy when very dry. Check out the Devils Garden Loop (6 miles) at dawn running past the main arches. Also, mountain bike ride the Arches National Park Loop, Warner Lake and Batchelor Basin. When forming loops that use the paved roads, keep in mind that the paved roads through Arches National Park are narrow and winding. They aren't the greatest for biking and the drivers can be distracked by the rock formations.
Overall, Arches National Park is the 36th most popular mountain bike trail of all 74 mountain biking rides in Utah.