Indoor tracks in Cheyenne; there are only 2 one is on F.E. Warren base at the 24 hour gym,(don't go to the wrong gym)and I have no idea how you would get on unless you have a good excuse for a visitors pass or if you know someone on base.
The second is at Cheyenne Central HS. I would ask the high school XC coach about getting on here, you might be able to jump in there when he hosts practice. His name is Rick and he owns foot of the rockies running store, very nice guy (2:19 marathoner at age 19)
You might not need an indoor though. It is very dry in SE WY and usually no snow on the tracks, maybe you can shovel it off if there is only a little.
Lions park and the greenway are the only runs in Cheyenne I would actually reccomend to anyone, ha. Enjoy it. There are very few runners in the town and people love to yell and throw things at you. Don't worry, it won't hit you because the wind will carry it away and they're to drunk to aim things well anyway! How i miss 100 MPW back home.