One thing not mentioned, your son needs to be 12 years old by the time the season opens to hunt big game in Wyoming. And any person born on or after Jan 1, 1966 (40 years old) must provide a hunter safety certificate of completion.
I strongly advise:
*Use of flat shooting calibers emntioned above. PRACTICE shooting out to 300 yards.
*Know your balistics. Bullet drop at certain yardages.
*Bring water jugs and cooler(s) big enough to hold 4 quarters, etc. because in order to fully appreciate Antelope meat at the dinner table, you should field dress it on site, skin it out, and wash it down good, then wrap in plastic and put on ice in cooler (not freezer). Otherwise, it can get gammey tasting and you've got 50 pounds of jerky.
*As mentioned, get aps in soon and be sure to check the "Party Application Block". This ensures that all who apply get a licence. All aps and instructions are available at the Wyoming G&F website.
As far as where? . . . The application allows you up to 3 choices. 1st, 2nd, 3rd. Because of the sheer number of animals, huge amounts of public land (BLM), liklyhood of drawing,and ease of access, I'd have to recommend an area called the Shirley Basin. Hunt area 47 covers most if not all of it. It is north of Medicine bow and south of Casper. The only downside is that there is not much more to eat there than sage brush and prarie grasses so some would say the diet adversly effects the taste of the meat. I don't necessarily agree. I believe quick and proper handling of the game is much more important than what it ate.

Pretty windy aren't I? Its usually windy here in Wyoming too!