The fictional locations
Naturally, the fictional locations can be different in the original novel The Virginian, written in 1902 when the old west was more current affairs than history, And in each and every movie adaptation, and in the TV series the Virginian.
In the introduction "To the Reader". Owen Wister says: "For Wyoming between 1874 and 1890 was a colony as wild as was Virginia one hundred years earlier. As wild, with a scantier population, and the same primitive joys and dangers. There were, to be sure, not so many Chippendale settees."
So the events in the novel happen sometime in the 16 years between 1874 and 1890, possibly during a significant fraction or even all of those 16 years.
The novel opens with the narrator arriving on a Union Pacific train at the town of Medicine Bow, Wyoming, a real town on the Union Pacific railroad line. The Union Pacific reach Laramie, east of Medicine Bow on June 7, 1868, and reached Fort Fred Steele, west of Medicine Bow, on July 21, 1868, so Medicine Bow was the westernmost station on the line for only a few weeks. The Union Pacific reached Evanston, in the southwestern corner of Wyoming, on December 4, 1868.
So if the Shiloh ranch was a great distance west of Medicine Bow, it would have been logical to get off the train at a more western station anytime in the period 1874 to 1890. But Medicine Bow, at 41 degrees, 53 minutes 52 seconds north, seems to be the northernmost Union Pacific station in Wyoming. So almost straight north from Medicine Bow would seem to be a logical direction for finding the Shiloh Ranch.
If one locates Rawlins, Medicine Bow, and Laramie on the map of Wyoming and draws large circles around them, a straight line between the two places were two of the circles overlap will be the line between the places that are closest to each of the towns. So a line from southeast to north west between Rawlins and Medicine Bow, and a line from southwest to northeast between Medicine Bow and Laramie, should mark the borders of the area that is closer to medicine Bow than any other Union Pacific station. Except that there may have been intermediate stations on the line in 1874-1890, which would reduce the size of the area closest to Medicine Bow.
Medicine Bow is 215 miles due south of the Wyoming-Montana border. But in Chapter Two the Virginian tells the narrator that the distance to the ranch is 263 miles. If the ranch was on the Wyoming-Montana border it would have to be 151.472 miles west of due north from Medicine Bow. Fortunately the Virginian could have meant that it was 263 miles as the various roads and watercourses they traveled along wound, instead of as the crow flies.