Haven't hunted in there in a lot of years but back in the late 90's took a cow off the rim of Alamo Canyon in the Dome Wilderness. A fire burned through the area in 1996 so it's mostly small trees and high grass. Watched a NMGF officer put down a nice 5x5 bull near Sawyer Mesa (it had been hit in an earlier season and my brother and I found it laying about a 100 yards off the road starving.). The Dome area is usually better for the late hunts (December...) after the elk start to move off the Valles Caldera towards the Bandelier National Monument.
Have also seen elk back up from Coyote/Youngsville but the road gets really rough.
One of the most important components of deciphering a new hunting area is distinguishing between the summer and winter ranges for the game that you plan to pursue. Without knowing this you cannot make reliable assumptions about where the game will be come opening day. Knowing these areas will allow you to take the current weather (as well as the past couple weeks) and apply that to the landscape and make an educated guess as to where you might find that big buck or bull.
There are a couple ways...