I have not been to Cheyenne during Frontier Days yet but started working for a company with offices here so I'm on my 9th trip so far, and have been keeping half an eye out because I want to bring the family out at some point this summer.
Not sure if there's true bookdocking BLM-style outside of town, but I know the Curt Gowdy campground (which looks fairly rustic) is not far away. There's also a couple of campgrounds I've eyeballed -- AB Camping on College, which looks nice at the first eyeball, and the KOA near Campstool Rd which is more of a parking lot but easy pull throughs for a DP.
At Campstool Rd. there's a Pilot/Flying J, as well as a dirt lot across the street from it where I see folks overnight all the time (RVs as well as trucks). Not sure if they gets full or if there would be issues for just parking there for multiple days during Frontier Days.
Perhaps someone else can chime in, but I figured I would toss in my two cents since no one else had responded.
The Green Machine -- 2000 Mountain High Coachworks Summit (Spartan chassis / Cummins ISC)
...and F-Troop: Fearghus, Fiona, and Frankie (Cairn Terriers)