Western romances are usually American historicals, set after the Civil War. From 1866 to about 1900 is the time frame. The stories revolve around either a cowboy or an Indian, during the days of the great push to "Go West!"
So think "Wild West" here. Wyatt Earp. Jesse James. Billy the Kid. These books take place between the Mississippi River and the Pacific Ocean. Books set on the Eastern seaboard isn't usually considered a "Western", because the term technically means "west" of the Mississippi.
So all the western states are pretty much fair game, from Kansas to Texas, to Montana, Wyoming, Utah, Colorado, Nevada, you get the idea.
Even a book set in San Francisco during the Gold Rush could be considered a western, because of the "lawlessness" that went on. Westerns usually have the stigma of being "wild" and "untamed", just as the country they are settling.
A book on the Oregon Trail, for example, would also be considered a western. Usually books about wide open skies, small, booming towns, sand and sage, and horsemen. You have to stear clear of any big cities in a western. You can start or end in one, but the majority of the story must be in the wilderness. A small town or a ranch is considered "the wilderness", because it's not in a big city. :P
Clear as mud?