The only firm dates in our travel window is the possibility of joining some friends in Cheyenne for a couple days during Frontier days at the end of July
For Cheyenne Frontier Days, unless you're staying on your friends' private property, or have reservations already, you will definitely need reservations...NOW. In addition to all of the attendees that will also be looking to stay in the area, you have to compete with the rodeo folks who are travelling that circuit in the summer months. This is particularly true for the weekends of CFD. I'm going to respond on the presumption that you don't have reservations already.
Likely that everything in the Cheyenne area is already booked, including all of the commercial parks as well as Curt Gowdy State Park to the west. Vedauvoo could be a possibility since it is first come/first served. You would likely need to get there on a Wednesday or Thursday to get a spot. Otherwise, look further out.
To the north are Glendo and Guernsey State Parks, about an hour or so north of Cheyenne. Both are very nice parks, with plenty to see and do on their own.
To the west there are commercial campgrounds/RV parks in Laramie, but there's also a good chance they are booked already, at least for the weekends. Laramie is about 45 minutes west of Cheyenne. Look further west, in the Centennial area, to the south and west. There's a bunch of wonderful USFS CG in that area, some that take reservations and some that are first come/first served. About 30-45 minutes further west from Laramie.
To the south into Colorado, there's a KOA outside of Wellington CO, but it has a lot of permanent residents who commute to Cheyenne. There's also another KOA in Fort Collins as well as to the northwest of Fort Collins in Laporte. Might be able to find space at either of these.
There's also Horsetooth Reservoir to the west of Fort Collins that has some wonderful camping, but it's very popular and reservations will likely be needed, weekends for sure. Further south, in Loveland is Boyd Lake State Park and even further south in Longmont is St. Vrain State Park. Reservations definitiely needed for weekends.
Northwest of Fort Collins along CO 14 in the Poudre Canyon, there are USFS CG that are a mix of reservations and first come/first served. These are also popular in season and reservations at the ones reservable are recommended. They are also further out from CFD, would take about 60-90 minutes or more to get to Cheyenne.
Whatever you decide, hope you have a wonderful trip.