The best area for trophy speedgoats would be the Red Desert. # 57, 60, 61 for a good area to see a lot of goats, look at the Cheyenne area, much of that area is private. The NE part of the state has plenty of public land and some goats too.
If you're wanting to hunt this year, there are some units that still have leftover tags - and some decent access, too
if you want to hunt speedgoats, you'll have to do a bit of crawling and sneaking - but don't worry, in most areas there are enough animals that if you blow a stalk, there will be another bunch just over the next rise!
One of the most important components of deciphering a new hunting area is distinguishing between the summer and winter ranges for the game that you plan to pursue. Without knowing this you cannot make reliable assumptions about where the game will be come opening day. Knowing these areas will allow you to take the current weather (as well as the past couple weeks) and apply that to the landscape and make an educated guess as to where you might find that big buck or bull.
There are a couple ways...