Jeep roads abound but I wasn't comfortable driving very far in my stock 4Runner alone because the sand is quite serious here; I walked the roads instead and even that was not easy! As I parked the car and began slogging through the deep sand a pack of coyotees were howling nearby, uncomfortably close. The named peaks, Elephant and Sandstone Buttes, were my main objective but I also ended up climbing two other unnamed summits nearby. On the cross country hike back to the car I was attacked by a vicious manzanita who cut my wrist very deeply and drew much blood. Damn manzanitas.
This is a beautiful area and all of the peaks were interesting. Elephant Butte and the unnamed mesa just east of it are guarded by fierce cliffs on every side and finding a suitable weakness takes some exploring.
Don't confuse this Elephant Butte with the Elephant Butte that is the highpoint of Arches National Park and an increasingly popular scramble.