Dos Cabezas is your best bet. After that would be the Peloncillos. Pedragosas have experienced sharp decline in population the last few years; likely due to drought, mountain lions, and hunt pressure.
The North end of the Mule Mtns will hold the highest number of deer but access is very difficult. You can get within a mile from the northwest base of the range by accessing the High Lonesome road from Davis Rd. Walk in from there. Glass the open grassy slopes and ridgelines. Bucks also like to hang out in ocotillo. Good luck.
West side of Chiricahuas is your best bet. Turkery Creek and Rock Creek have good access but lot's of hunters. However, if you go all the way to the end of Rock Creek road and then hike in about 2-3 miles you should be away from most of the pressure. Glass open ridgelines all morning and all evening. Good luck.