We generally hunt the foothills and flats but will go up in the mountains sometimes. Lots of deer in the Dunken and Pinion area. If you can find public access close to the Penasco river area it ought to be money. The deer like the valley land around the Penasco river for the irrigated farms that provide good food source.
The Queen area is a good area. Quickly after turning onto the south rim road, you will come to "Cougar" road. Turn left. If you take the first left it goes to a windmill. Park at the windmill and walk back towards highway 137.
You can also take the 3rd left off of Cougar road, the road begins with a barbwire gate next to a big tree, and goes back in towards Queen with a windmill about halfway through, good area to hunt.
Also check County Rd 64 which runs north off of 137 by Queen. Usually deer there as well. You can also go South of Queen to town toward Dell City and hunt Crow Flats-Humphries Canyon area.
Try the foothills and canyons east of hwy 137 near Cone Butte, and Tom's Canyon, also the foothills on the north end of the Guads south of Hope.
You can also try the Brokeoff Mountains by Dell City. It's a rugged area. I've seen some deer there but some years I haven't, but worth scouting.
One area I've killed a 29 inch Mulely was Sitting Bull Falls area Southwest of Carlsbad. This area can be hit or miss but holds some big ones at times.
Also check around Marathon coming in off Armstrong road. Head to Little Box Canyon and Box Canyon. Always see deer in this area. Scout the area between Hope and the Armstrong Ranch, deer always in that area.