I know that in Wyoming, if you call the field offices, they have landowner lists for those that allow hunting on their property. Also there is plenty of BLM ground in Wyoming that doesn't require preference points to draw. The area me and my brother hunted last year (21) was one of those areas. Neither one of us had ever been there before and both killed out by the second day of the season.
Just go to the Wyoming game and fish website and look at the draw odds for each area. Pay close attention to the areas with the little * next to them. Those are the areas that don't have a lot of public ground, which means they have a pretty good draw odds. Then go to the BLM website and look at the maps and see exactly how much or how little is there.
Hopefully MachV chimes in, as he seems to have a lot of expertise when it comes to Wyoming goats.
Good Luck