If your travel time is flexible, there are several shuttles that run from Cheyenne to neighboring cities, such as Denver, Casper, Fort Collins, and Laramie. The fares are usually very reasonable (something like $35 one-way to Denver), and they often have a daily run, although some may be weekly. Look in the Yellow Pages for "Shuttle". (Dex is the local Yellow Pages for Cheyenne).
This can change at a moment's notice, but generally speaking, this location has been about the lowest price gasoline in the area. It's the "TA" station right next to Interstate 80, about 17(?) miles east of Cheyenne. I do know that you take exit 377 to access the station.
CHEYENNE HAS A NICE REST STOP AND INFORMATION CENTER located on the west side of Interstate 25.
Look for a big "Flying J" truck stop on the west side and the rest stop will be directly north of that.
(Take the exit at the Flying J and you will get to the rest stop.)
IF YOU GET OFF THE INTERSTATE AND ONTO HIGHWAY 30, it will take you right into Cheyenne.
This is the view coming from the east.