I am a Wyoming native of Washakie County and spent several years of my life hunting, fishing, camping and hiking in the Big Horn Mountain range of North Central Wyoming. My uncle owned an "outfitters" ranch in the Paintrock Basin of the Big Horns and my family and I are quite familiar with the area.
Although there is no "Brokeback" mountain there, there is however a Brokenback Mountain and a Break Back Mountain. Not named after a particular mountain but after the surroundings and how treachorous and difficult it is to get around there. The closest town to Brokenback mountain is Tensleep, Wyoming, which is a very small town.
You can go to this link and it will provide more information on the area:
and here is a news story out of Kansas that has some information on it:
Hope that helps!
A Wyoming Native