Well, here are a couple ideas:
Visit the Cheyenne Botanical Garden. It is located in Lions Park across from the Frontier Days rodeo arena. While not huge, it is large enough that you can spend a couple hours touring the grounds, and there might be a few things you'd still miss in that time. I went there last month with my kids, and though they weren't as interested as I was, they did find it interesting at times. I thought it was a beautiful place, and also liked the passively heated greenhouse, which is something I hope to build on my own property sometime. I wanted to get some ideas for when I do that.
You can also visit the Frontier Days museum, next to the rodeo arena, and across the street from the Botanical Garden mentioned above. Both of these places have websites you can see to get more information.
Cheyenne Botanic Gardens: is the link for the garden.
Cheyenne Frontier Days Old West Museum is the link for the museum.
If you're into hiking and that sort of outdoor activity, you can go to Vedauwoo Recreation Area or Curt Gowdy State Park, both west of Cheyenne.
Dave's Wallpaper - Vedauwoo - Medicine Bow National Forest - Laramie, Wyoming this link has some info and a bunch of great pictures.
Wyoming Curt Gowdy State Park - WyomingTourism.org this is a link about the State Park.
If you like old trains, there is a "Big Boy" locomotive on display in Holladay Park. More info about this, and many other things can be found at this website:
Welcome to Cheyenne, Wyoming
Good luck on your travel plans, and have a great time when you visit Cheyenne.