You should have no problem getting a tag. Basically use I-25 to cut the state in half, everything East of it is pretty good goat hunting. As you get to Casper the goats spread to the West making Natrona, Carbon, and Albany counties pretty good. Your problem will be ground to hunt. Permission can be tough, a lot of these old ranchers have gotten their fingers burnt from "Out of Staters'" and won't whiz on you if you were on fire. Public ground is that, and be prepared to enjoy your hunt with 150 of you closest new friends from WI, MI, MO, MS, etc, etc.
Try and get you a tag. Come out and get a feel for the country. With hat in hand and asking nicely, some good ol' boy might let you let the air out of a "Range Maggot" on his place.
Oh, and watch for rattlesnakes