I am from Wyoming and I don't know exactly how the out of state draw is run, but as far as sear numbers and size. You can't beat Cambell County, or Gillette, Wyoming. I work out in the oil and gas field and I spend 10 hours aday running around all over North East Wyoming. This year was one of our best years for antelope. I got the chance to take one over 70 inches on public land. I only two days to hunt, there were many nice bucks to look over.
I would tell you area 23 is a good area, which is along the west side of Gillette and it runs out to the powder river. It's a large area with lots of public land. I know a guy could pick up a few buck tags and at least 4 doe tags. This year there were many left over tags that could be purchased over the counter by out of state hunters, doe and buck, and for nearly every area. If by some rare chance you don't draw a antelope tag, check with Game & Fish and ask them how many additional tags are left over. You can almost always purchase these after the draw. I think now you can even do it online.
Public land deer is another subject, the best chance at killing a large mule deer on public land is going to be in your special draw area offering only a few tags. There are some really good areas around Laramie and Jackson Hole but your going to have horses to get to them areas. It's all in what your looking for. There are alot of public areas in the North East and South West Wyoming.
I only have knowledge of the North East, for mule dear the later in the season the better. Which doesn't really work good for doing a combo hunt. The Black Hills of Eastern Wyoming are great because Muleys don't get near the pressure, every one is out to kill a Whitetail. If you have any questions feel free to drop me a email firstname.lastname@example.org
I always like to help other hunters out.