I live in Laramie which is on the border of region D. There is a ton of public land out in the Snowy Range which would be areas: 75, 76, 78, and 79. Easy access to most of the area as there are roads in it, but also lots of trails where you can get away from people. I have seen deer out there but not very many nice bucks. The winter here has not been to bad, we don't have much snow and it hasn't been as cold as years past. So there is a chance you could find some very nice deer in the area. There are also a few wilderness areas up there, and you cant take any mechanical vehicles into them. I have been out in this region this winter a few times and have seen some dang nice deer that I would not pass up, but while hunting I have not seen these deer.
I also have spent a little time in area E and most of it is out on the high desert it looks like from the map. I have always been hunting antelope. I have not seen any deer out there the few times I've been there but you might have some luck over by Lander. I can't say much about this region because I have never hunted it for deer.
So if it was my decision I would probably go with region D, just because I have more experience with that region. It also depends on the kind of hunting you will be doing. From the deer I have seen out on the winter range this year I might even try to hunt over here this year. I usually hunt the other side of the state, but last winter really killed the deer over there. I'm hoping to get out and do some more scouting this summer, to see if I can find and good deer anywhere.
Hope this helps.