Advice from a 38 year Wyoming resident who has guided and hunted Lopes for years: In Wyoming, there are more Antelopes than people! They are everywhere. So . . . I advise you find areas with large amounts of public lands, few hunters, and nearby town for lodging, supplies, etc.
My first area meeting these criteria would be 53. Lots of goats and some huge ones! South central WY just north of Baggs. Go to:
http://wgfd.wyo.gov/web2011/hunting-1001080.aspx and absorb all you can. Check out the "land status map". The white areas are private. The gold, blue, green areas are BLM, State, and Nat'l Forest public lands!
Remember . . . Wyoming is mostly public land! DON'T PAY A TRESPASSING FEE! All landowners I have talked to are eager to get rid of the pesky little bastards! And they get $16.00 (landowners coupon) for every goat taken off their land. Also, be aware there are provisions to apply for more than one area to hunt called "Combined Hunt Areas". I don't know how to apply for this, but it allows a person to hunt more than one area even though they have drawn for only one. Call the G&F to get better answers.
Most importantly . . . practice shooting at least to 500 yards. I know, I know, that sounds like a lot. It is in GA. but not out here. I'm not suggesting you take a 500 yard shot, but if you practice FAR, you can hit close a lot more effectively. Besides, it's really fun! Good luck and do get some "reduced price doe/fawn tags" to put more meat in the freezer.