Curt Gowdy State Park is about halfway between Cheyenne and Laramie. I always liked the area around the Upper North Crow Reservoir.
Curt Gowdy
Vedauwoo is also an interesting place West of Cheyenne. The site shows rock climbing in detail but there is plenty of hiking around Vedauwoo
Vedauwoo
There is a small chunk of the Medicine Bow National Forest just East of Laramie (about 45 minutes to the West of Cheyenne on I-80). Take I-80 out of Cheyenne heading W/B then take the Sherman Pass (Lincoln Memorial) exit onto Happy Jack Road. Take Happy Jack back toward Cheyenne. Take any of the dirt roads off of Happy Jack in the forest to find some hiking. Here's a map that should give you some places to explore.
USFS Happy Jack Pole Mountain
I grew up in Cheyenne and went to college in Laramie. This was my playground as an outdoorsy teen.
Be safe.