Much of Brokeback Mountain is set in Riverton, Wyoming, gateway to the Wind River Range and Gannett Peak.
However according to the IMDB, the “gay cowboy flick” was made in the Canadian Rockies near Calgary, Albert; Fort Macleod in Alberta and La Mesilla, New Mexico.
The USGS Global Names Information System shows no Brokeback Mountain although there is a Brokenback Creek/Narrows/Reservoir about 100 miles northeast of Riverton.
Annie Proulx was quoted in Planet Jackson Hole:
Brokeback is not a real place. There is, on a map I once saw, a Break Back Mountain in Wyoming which I have never seen, but the name worked on several levels and replaced half a dozen more pedestrian names I had been trying out.
However a check of the USGS database showed now Break Back Mountains in Wyoming — although there are plenty of Breakneck features in Wyoming and elsewhere.
Brokeback would seem like a good name for a mountain but I could not easily find it via Google although there is a Brokenback mountain range in Australia.
According to the USGS there are only two summits which are similarly named
Allthough there’s a lot of broken features out there include Broken Mountain (AK), Broken Finger (CA), Broken Hill (CA/NV), Broken Rib (CA), Broken Hand(CA/CO), Broken Crater (ID), Broken Top (ID), Broken Leg (MT), Broken Bone (ND), Broken Ground (NH), Broken Back Crater (NM), Broke Off (NM).
Riverton is depicted in the movie as a dreary wide spot in the road with a delapidated one-room post office — not a “booming” college town of 10,000 with an airport with commercial service. Although it’s a big town for Ennis Del Mar (the Heath Ledger character) who moves there from a ranch with his wife so they can be around other people.