Never hunted there, but I have spent a decent amount of time in the area.

Mountains to the south and west. There are some big elk and some big mulies in the mountains and the foothills. There are also a ton of grizzlies and wolves. Pack pepper spray and/or a firearm. To the south near Meeteetsee in the foothills there are some big deer as well, but the tag is hard to draw and most of the land is private. There are some antelope to the east of town in the desert. If you can draw the tag, there are bighorn sheep in the mountains and mountains goats as well. Same goes for moose. Not a whole lot in the way of waterfowl hunting, but there are some birds around. If you're big into waterfowl, you'll have a lot more luck in the Bighorn River by Thermopolis. There are chuckars and huns in the area as well. And if you want a change of scenery, the Bighorn mountains are not far to the east. The local Game and Fish office could probably tell you more than I can.

If I were you, I'd make friends with someone who has horses real quick so that you can pack back into the mountains and take a crack at a trophy bull elk.

Also, though not hunting related, rafting/kayaking on the Shoshone River that runs through the edge of town is a lot of fun. A few of the waves get really good during runoff when the water is high, and its a good way to stay cool during the summer. Most people put in to the west of WalMart at the end of a dirt road (can't remember the name of the road) and take out below the bridge on the highway to Powell.