I know the area.
If you are needing a place to hunt, access will be the biggest problem, unless you have private property lined up. There are always leftover tags in those areas because of the access issue. Last year I saw a guy get a tresspassing ticket for being about 40 feet on the wrong side of the property line. He was trying to work a small piece of public ground and strayed over. Had his young teenage boy with him, so it made it tough. Remember, there are not a lot of fences to mark the boundaries, so you better know where you are at.
The trouble with the public spots in that area is that they tend to be small, real small by western standards. And they are irregular shaped which can make navigating a nightmare if you are not used to map reading. And there is not a lot in the region, so those small spots get hit really hard by nonres and locals. Deer zones 163 & 169 only have a week-long season because of the pressure. May be the only 2 zones in the state with such a short season. You will often hear "Wait till after opening week and then the pressure lets up", but opening week is the ONLY week in those two deer zones, which have the most public land in that part of your region Y tag. Some of the big chunks of public ground (like many other zones in that part of Wyoming) are not accessible from a public road, so you have to have permission (read that "open your wallet") from the landowner to get to them. Several of the roads in that area are not public roads.
I would describe the antelope population as good and the mule deer population as fair. I would say it is not an area known for trophys, but the potential always exist. I am sure someone can show you a picture of a monster that came from those areas, it's just that there are better areas for both, population and trophy potential wise.
Now, all that being said, you already have the tags and there are definitely deer and antelope there, so go have a blast. I am not trying to rain on your parade, just telling you how it is. The nice thing with your "region" deer tag is that you can always move to another zone up north if you want to. You are not limited to only one zone as with the antelope tag. The Big Horns offer a large piece of ground to hunt within your region if you need places to go. The good thing with your zone 21 antelope tag (which encompasses deer zones 163 & 169 with their public lands)is that the antelope season is runs long, not just a week like the deer season does.