There are elk in the Snowy Mountains, but in a general hunting season you‘re sharing it with crowds from Laramie and Cheyenne. There is mule deer hunting in the Snowies, but you have to hunt around large patches of private ranch land to access much of it.
As a kid full of energy, in great shape and a month off ever fall I hunted general admission areas in the Snowies hard for half a dozen years - time is much better spent in either harder to draw limited quota areas, or the western part of the state. Leaving Laramie at 3:00pm Friday afternoon and setting up camp at 11:00, and hunting first thing Saturday morning doesn’t seem too bad to me.
The sagebrush and foothill/aspen country closer to Rawlins always produces some big racks each year - that’s where the locals in Rawlings hunt.
The limited quota sagebrush elk herds have high success - reminds me of antelope hunting.
Stay away from casper mountain.
If you just want to kill something, pay one of the ranches and shoot a cow elk off their haystack in a late season.