I mostly grew up in Casper, I have lived there about 9 times at varrying intervals and my parents still live there, or live there again as it were.
Casper Mountain has a small ski area called Hogadon, and a wonderful snowmobile area in Bear Trap Meadow if you like to play in the snow.
The North Platte River in Casper is Blue Ribbon, and there are several outstanding flyfishing shops in town, the lower section of the river has a million dollar whitewater park improvement on it, and the upper section is set up for drift boats.
Pronghorns and mule deer are all over town, with a few whitetails and wild turkeys.
Casper Events Center host the 2nd or 3rd last pro NFR Rodeo qualifier in November for a week, and the College National Finals Rodeo is also held in Casper.
While Casper mountain is short on public land and elk, the mountain behind it is **** near all BLM/Forest Service Muddy Mountain and has a lot of elk.
Houses are expensive compared to most other parts of the state (excepting Jackson). But you will have lots of choices.
My parents live on the West side of town right before the Canyon narrows. They have 5 acres, barn, shop, and a new manufactured home and I think they have about a $280,000 property. It was just dirt and sage brush when they got there. They probably spent $170,000 on it.
As far as shooting goes there are a lot of choices. Poison Spider 1000 yard range, an indoor pistol range, a Blackpowder range in Glenrock, the City Range at Stuckenhoffs, and lots of BLM areas that people have turned into ranges. There are more but I can't remember all of them.
Rocky Mountain Sports is always worth a visit, nice selection of everything and often some good high end stuff. Sportsman's Warehouse, lots of pawn shops, and some good gunsmiths.
Dale Story is probably the best gunsmith in town, and if you drive out to Glenrock you have A-Square, Glenrock Blue, and Glenrock Reloading. So lots of choices.
Both Alcova and Pathfinder lakes have really good walleye fishing if you have a boat.
Alcova lake is canoeable. Pathfinder is very nasty with the winds. Sometimes Pathfinder isn't safe even on a big center console Alaska type boat.
Denver is about 5 hours, and Billings is about 3 or 4, Salt Lake is about 6 or 7 hours, and Reno is another 5 beyond Salt Lake.