I'd rather not talk about the movies I watch when I stay at a Best Western.
If I had to choose one it would be "The Man Who Shot Liberty Valance".
High Noon but other faves are Unforgiven and the Searchers. Actually the best western is not a western but has a similar story arc and was copied into a western and that is the Seven Samurai!
Rio Bravo with John Wayne, Dean Martin, Walter Brennan and Ricky Nelson is a classic, and always a favorite of mine. Tombstone, as you have mentioned, is always great.
I thought Appaloosa with Ed Harris that came out a year or two ago was pretty enjoyable.
How about the Searchers, Wild Bunch and Tombstone. And last but certainly not least the Unforgiven. IMHO!!!
High Noon.