I haven't been in the area now for over 10 years but suppose the speed goats hang out in the same areas.
The first place I would try is the big ridge south of the Burns Brothers Truckstop West of Fort Bridger. It has a lot of sage on it and I have seen quite a few goats there. If that does not pan out hunt the valley at the bottom of that ridge to the West. I used to get permission from the ranchers to hunt antelope. That main gravel road will take you clear to Evanston. I have seen plenty of antelope south of I-80 between Fort Bridger and Evanston. Just keep at it and you should have success.
Another area you might want to check out is the big sagebrush flats between Mountian View and Lone Tree. South side of the highway.
Make sure you check land ownership maps. Area 99 has a lot of private property. You used to be able to get permission pretty easy though.