Castleton Tower is probably the most famous desert tower in the world, and was the first major tower climbed in the Moab area. The Kor-Ingalls route is one of the 50 Classic Climbs of North America, and Castleton also has one other 5.9 route of the same caliber. Harder classic routes both aid and free exist on its fantastic Wingate sandstone with its unique calcite crust (from Mountain Project website). There is a small (free) campground on private land adjacent to the approach trail for the climb.
From Moab, Utah, drive 15.5 miles on SR 128 and turn right onto the Castle Valley road. Proceed another 4.6 miles. You will find the campground on Castle Valley road about 1/4 to a 1/2 mile after the cattle guard in the road on the left. From the campground/parking lot hike up the wash following the cairns until you get to a dirt road. Cross this road at a cairn and a signpost with an arrow pointing along the trail.